x^2+128=23x+8

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Solution for x^2+128=23x+8 equation: 


Simplifying
x2 + 128 = 23x + 8

Reorder the terms:
128 + x2 = 23x + 8

Reorder the terms:
128 + x2 = 8 + 23x

Solving
128 + x2 = 8 + 23x

Solving for variable 'x'.

Reorder the terms:
128 + -8 + -23x + x2 = 8 + 23x + -8 + -23x

Combine like terms: 128 + -8 = 120
120 + -23x + x2 = 8 + 23x + -8 + -23x

Reorder the terms:
120 + -23x + x2 = 8 + -8 + 23x + -23x

Combine like terms: 8 + -8 = 0
120 + -23x + x2 = 0 + 23x + -23x
120 + -23x + x2 = 23x + -23x

Combine like terms: 23x + -23x = 0
120 + -23x + x2 = 0

Factor a trinomial.
(8 + -1x)(15 + -1x) = 0


Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

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 = {8, 15}

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