x(x-5)=5(x-5)

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Solution for x(x-5)=5(x-5) equation:


Simplifying
x(x + -5) = 5(x + -5)

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

Reorder the terms:
-5x + x2 = 5(-5 + x)
-5x + x2 = (-5 * 5 + x * 5)
-5x + x2 = (-25 + 5x)

Solving
-5x + x2 = -25 + 5x

Solving for variable 'x'.

Reorder the terms:
25 + -5x + -5x + x2 = -25 + 5x + 25 + -5x

Combine like terms: -5x + -5x = -10x
25 + -10x + x2 = -25 + 5x + 25 + -5x

Reorder the terms:
25 + -10x + x2 = -25 + 25 + 5x + -5x

Combine like terms: -25 + 25 = 0
25 + -10x + x2 = 0 + 5x + -5x
25 + -10x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
25 + -10x + x2 = 0

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


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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {5, 5}

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