-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 = 1x2
12 + -7x + 1x2 = 6x + -3x2 + -6x + 3x2

Reorder the terms:
12 + -7x + 1x2 = 6x + -6x + -3x2 + 3x2

Combine like terms: 6x + -6x = 0
12 + -7x + 1x2 = 0 + -3x2 + 3x2
12 + -7x + 1x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
12 + -7x + 1x2 = 0

Factor a trinomial.
(3 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {3, 4}

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