3x^2+13x-7=2x^2+7x-12

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Solution for 3x^2+13x-7=2x^2+7x-12 equation: 


Simplifying
3x2 + 13x + -7 = 2x2 + 7x + -12

Reorder the terms:
-7 + 13x + 3x2 = 2x2 + 7x + -12

Reorder the terms:
-7 + 13x + 3x2 = -12 + 7x + 2x2

Solving
-7 + 13x + 3x2 = -12 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-7 + 12 + 13x + -7x + 3x2 + -2x2 = -12 + 7x + 2x2 + 12 + -7x + -2x2

Combine like terms: -7 + 12 = 5
5 + 13x + -7x + 3x2 + -2x2 = -12 + 7x + 2x2 + 12 + -7x + -2x2

Combine like terms: 13x + -7x = 6x
5 + 6x + 3x2 + -2x2 = -12 + 7x + 2x2 + 12 + -7x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
5 + 6x + 1x2 = -12 + 7x + 2x2 + 12 + -7x + -2x2

Reorder the terms:
5 + 6x + 1x2 = -12 + 12 + 7x + -7x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
5 + 6x + 1x2 = 0 + 7x + -7x + 2x2 + -2x2
5 + 6x + 1x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
5 + 6x + 1x2 = 0 + 2x2 + -2x2
5 + 6x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + 6x + 1x2 = 0

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


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

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

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

Simplifying
x = -5

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-5, -1}

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