(x-5)=x^2-8x+15

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Solution for (x-5)=x^2-8x+15 equation: 


Simplifying
(x + -5) = x2 + -8x + 15

Reorder the terms:
(-5 + x) = x2 + -8x + 15

Remove parenthesis around (-5 + x)
-5 + x = x2 + -8x + 15

Reorder the terms:
-5 + x = 15 + -8x + x2

Solving
-5 + x = 15 + -8x + x2

Solving for variable 'x'.

Reorder the terms:
-5 + -15 + x + 8x + -1x2 = 15 + -8x + x2 + -15 + 8x + -1x2

Combine like terms: -5 + -15 = -20
-20 + x + 8x + -1x2 = 15 + -8x + x2 + -15 + 8x + -1x2

Combine like terms: x + 8x = 9x
-20 + 9x + -1x2 = 15 + -8x + x2 + -15 + 8x + -1x2

Reorder the terms:
-20 + 9x + -1x2 = 15 + -15 + -8x + 8x + x2 + -1x2

Combine like terms: 15 + -15 = 0
-20 + 9x + -1x2 = 0 + -8x + 8x + x2 + -1x2
-20 + 9x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
-20 + 9x + -1x2 = 0 + x2 + -1x2
-20 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + 9x + -1x2 = 0

Factor a trinomial.
(-5 + x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

Subproblem 2
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
Solution
x = {5, 4}

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