-2x^2-x+12=3x^2+6x

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Solution for -2x^2-x+12=3x^2+6x equation: 


Simplifying
-2x2 + -1x + 12 = 3x2 + 6x

Reorder the terms:
12 + -1x + -2x2 = 3x2 + 6x

Reorder the terms:
12 + -1x + -2x2 = 6x + 3x2

Solving
12 + -1x + -2x2 = 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
12 + -1x + -6x + -2x2 + -3x2 = 6x + 3x2 + -6x + -3x2

Combine like terms: -1x + -6x = -7x
12 + -7x + -2x2 + -3x2 = 6x + 3x2 + -6x + -3x2

Combine like terms: -2x2 + -3x2 = -5x2
12 + -7x + -5x2 = 6x + 3x2 + -6x + -3x2

Reorder the terms:
12 + -7x + -5x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
12 + -7x + -5x2 = 0 + 3x2 + -3x2
12 + -7x + -5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
12 + -7x + -5x2 = 0

Factor a trinomial.
(1 + -1x)(12 + 5x) = 0


Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(12 + 5x)' equal to zero and attempt to solve:

Simplifying
12 + 5x = 0

Solving
12 + 5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + 5x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 5x = 0 + -12
5x = 0 + -12

Combine like terms: 0 + -12 = -12
5x = -12

Divide each side by '5'.
x = -2.4

Simplifying
x = -2.4
Solution
x = {1, -2.4}

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