x^2-2x-32=4x-5

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Solution for x^2-2x-32=4x-5 equation: 


Simplifying
x2 + -2x + -32 = 4x + -5

Reorder the terms:
-32 + -2x + x2 = 4x + -5

Reorder the terms:
-32 + -2x + x2 = -5 + 4x

Solving
-32 + -2x + x2 = -5 + 4x

Solving for variable 'x'.

Reorder the terms:
-32 + 5 + -2x + -4x + x2 = -5 + 4x + 5 + -4x

Combine like terms: -32 + 5 = -27
-27 + -2x + -4x + x2 = -5 + 4x + 5 + -4x

Combine like terms: -2x + -4x = -6x
-27 + -6x + x2 = -5 + 4x + 5 + -4x

Reorder the terms:
-27 + -6x + x2 = -5 + 5 + 4x + -4x

Combine like terms: -5 + 5 = 0
-27 + -6x + x2 = 0 + 4x + -4x
-27 + -6x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-27 + -6x + x2 = 0

Factor a trinomial.
(-3 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-3, 9}

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