3x^2+3x-10=x^2-2x-12

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Solution for 3x^2+3x-10=x^2-2x-12 equation: 


Simplifying
3x2 + 3x + -10 = x2 + -2x + -12

Reorder the terms:
-10 + 3x + 3x2 = x2 + -2x + -12

Reorder the terms:
-10 + 3x + 3x2 = -12 + -2x + x2

Solving
-10 + 3x + 3x2 = -12 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-10 + 12 + 3x + 2x + 3x2 + -1x2 = -12 + -2x + x2 + 12 + 2x + -1x2

Combine like terms: -10 + 12 = 2
2 + 3x + 2x + 3x2 + -1x2 = -12 + -2x + x2 + 12 + 2x + -1x2

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

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

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

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

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

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

Factor a trinomial.
(2 + x)(1 + 2x) = 0


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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-2, -0.5}

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