x^2-6x+2x-3=9x+27

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Solution for x^2-6x+2x-3=9x+27 equation: 


Simplifying
x2 + -6x + 2x + -3 = 9x + 27

Reorder the terms:
-3 + -6x + 2x + x2 = 9x + 27

Combine like terms: -6x + 2x = -4x
-3 + -4x + x2 = 9x + 27

Reorder the terms:
-3 + -4x + x2 = 27 + 9x

Solving
-3 + -4x + x2 = 27 + 9x

Solving for variable 'x'.

Reorder the terms:
-3 + -27 + -4x + -9x + x2 = 27 + 9x + -27 + -9x

Combine like terms: -3 + -27 = -30
-30 + -4x + -9x + x2 = 27 + 9x + -27 + -9x

Combine like terms: -4x + -9x = -13x
-30 + -13x + x2 = 27 + 9x + -27 + -9x

Reorder the terms:
-30 + -13x + x2 = 27 + -27 + 9x + -9x

Combine like terms: 27 + -27 = 0
-30 + -13x + x2 = 0 + 9x + -9x
-30 + -13x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-30 + -13x + x2 = 0

Factor a trinomial.
(-2 + -1x)(15 + -1x) = 0


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

Simplifying
-2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-2, 15}

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