x^2+3x-12=9x-5

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Solution for x^2+3x-12=9x-5 equation: 


Simplifying
x2 + 3x + -12 = 9x + -5

Reorder the terms:
-12 + 3x + x2 = 9x + -5

Reorder the terms:
-12 + 3x + x2 = -5 + 9x

Solving
-12 + 3x + x2 = -5 + 9x

Solving for variable 'x'.

Reorder the terms:
-12 + 5 + 3x + -9x + x2 = -5 + 9x + 5 + -9x

Combine like terms: -12 + 5 = -7
-7 + 3x + -9x + x2 = -5 + 9x + 5 + -9x

Combine like terms: 3x + -9x = -6x
-7 + -6x + x2 = -5 + 9x + 5 + -9x

Reorder the terms:
-7 + -6x + x2 = -5 + 5 + 9x + -9x

Combine like terms: -5 + 5 = 0
-7 + -6x + x2 = 0 + 9x + -9x
-7 + -6x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-7 + -6x + x2 = 0

Factor a trinomial.
(-1 + -1x)(7 + -1x) = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1, 7}

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