x^2-5x+32=8x-4

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Solution for x^2-5x+32=8x-4 equation: 


Simplifying
x2 + -5x + 32 = 8x + -4

Reorder the terms:
32 + -5x + x2 = 8x + -4

Reorder the terms:
32 + -5x + x2 = -4 + 8x

Solving
32 + -5x + x2 = -4 + 8x

Solving for variable 'x'.

Reorder the terms:
32 + 4 + -5x + -8x + x2 = -4 + 8x + 4 + -8x

Combine like terms: 32 + 4 = 36
36 + -5x + -8x + x2 = -4 + 8x + 4 + -8x

Combine like terms: -5x + -8x = -13x
36 + -13x + x2 = -4 + 8x + 4 + -8x

Reorder the terms:
36 + -13x + x2 = -4 + 4 + 8x + -8x

Combine like terms: -4 + 4 = 0
36 + -13x + x2 = 0 + 8x + -8x
36 + -13x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
36 + -13x + x2 = 0

Factor a trinomial.
(4 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, 9}

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