-12+4x+3+5x=2x^2-6x-2

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Solution for -12+4x+3+5x=2x^2-6x-2 equation: 


Simplifying
-12 + 4x + 3 + 5x = 2x2 + -6x + -2

Reorder the terms:
-12 + 3 + 4x + 5x = 2x2 + -6x + -2

Combine like terms: -12 + 3 = -9
-9 + 4x + 5x = 2x2 + -6x + -2

Combine like terms: 4x + 5x = 9x
-9 + 9x = 2x2 + -6x + -2

Reorder the terms:
-9 + 9x = -2 + -6x + 2x2

Solving
-9 + 9x = -2 + -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
-9 + 2 + 9x + 6x + -2x2 = -2 + -6x + 2x2 + 2 + 6x + -2x2

Combine like terms: -9 + 2 = -7
-7 + 9x + 6x + -2x2 = -2 + -6x + 2x2 + 2 + 6x + -2x2

Combine like terms: 9x + 6x = 15x
-7 + 15x + -2x2 = -2 + -6x + 2x2 + 2 + 6x + -2x2

Reorder the terms:
-7 + 15x + -2x2 = -2 + 2 + -6x + 6x + 2x2 + -2x2

Combine like terms: -2 + 2 = 0
-7 + 15x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2
-7 + 15x + -2x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
-7 + 15x + -2x2 = 0 + 2x2 + -2x2
-7 + 15x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-7 + 15x + -2x2 = 0

Factor a trinomial.
(-7 + x)(1 + -2x) = 0


Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

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 = {7, 0.5}

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