x(x-5)=4(x-5)

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Solution for x(x-5)=4(x-5) equation: 


Simplifying
x(x + -5) = 4(x + -5)

Reorder the terms:
x(-5 + x) = 4(x + -5)
(-5 * x + x * x) = 4(x + -5)
(-5x + x2) = 4(x + -5)

Reorder the terms:
-5x + x2 = 4(-5 + x)
-5x + x2 = (-5 * 4 + x * 4)
-5x + x2 = (-20 + 4x)

Solving
-5x + x2 = -20 + 4x

Solving for variable 'x'.

Reorder the terms:
20 + -5x + -4x + x2 = -20 + 4x + 20 + -4x

Combine like terms: -5x + -4x = -9x
20 + -9x + x2 = -20 + 4x + 20 + -4x

Reorder the terms:
20 + -9x + x2 = -20 + 20 + 4x + -4x

Combine like terms: -20 + 20 = 0
20 + -9x + x2 = 0 + 4x + -4x
20 + -9x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
20 + -9x + x2 = 0

Factor a trinomial.
(4 + -1x)(5 + -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 '(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 = {4, 5}

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