1
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Rewrite the equation 6x^2 + 3 = 2x - 6 in standard form and identify a, b, and c.

2
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So standard form for a quadratic equation is ax squared plus bx plus c is equal to zero.

3
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So essentially you wanna get all of the terms on the left-hand side,

4
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and then we want to write them so that we have the x terms...where their exponents are in decreasing order.

5
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So we have the x squared term and then the x term and then we have the constant term.

6
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So let's try to do this over here.

7
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So let me rewrite our original equation.

8
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We have 6x squared plus 3 is equal to 2x minus 6.

9
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So essentially we wanna get everything on the left-hand side.

10
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so I could subtract 2x from both sides, so I could subtract 2x from both sides,

11
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so let me just...I'll take one step at a time.

12
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So I can subtract 2x from both sides.

13
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And then I'll get...and I'm gonna write it in descending order for the exponents on x.

14
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So the highest exponent is x squared. So I'll write that first.

15
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6x squared, and then we have minus 2x, and then we have plus 3 is equal to...

16
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the 2 'x's on the right cancel out...equal to negative 6.

17
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And now, to get rid of this negative 6 on the right-hand side, we can add 6 to both sides.

18
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So let's add 6 to both sides...

19
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...and then this simplifies to 6x squared, minus 2x, plus nine is equal to...zero.

20
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So let's make sure we're already in standard form.

21
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All of our terms, our non-zero terms are on the left-hand side, we've done that.

22
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We have a zero on the right-hand side, we've done that.

23
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And, we have the x squared term first, then the x to the first power term, then the constant term.

24
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x squared, then x to the first, then the constant term.

25
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So we are in standard form.

26
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And so we can say that a is equal to 6, a is equal to 6.

27
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We could say that b is equal to, and this is key, it's not just the 2, it's the negative 2.

28
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B is equal to negative 2, 'cause notice this says plus bx, but over here we have minus 2x.

29
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So the b is a negative 2 here. B is negative 2.

30
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And then c, c is going to be, c is going to be 9.