0=(4x-4)(x-5)

Solution for 0=(4x-4)(x-5) equation:

Simplifying
0 = (4x + -4)(x + -5)

Reorder the terms:
0 = (-4 + 4x)(x + -5)

Reorder the terms:
0 = (-4 + 4x)(-5 + x)

Multiply (-4 + 4x) * (-5 + x)
0 = (-4(-5 + x) + 4x * (-5 + x))
0 = ((-5 * -4 + x * -4) + 4x * (-5 + x))
0 = ((20 + -4x) + 4x * (-5 + x))
0 = (20 + -4x + (-5 * 4x + x * 4x))
0 = (20 + -4x + (-20x + 4x2))

Combine like terms: -4x + -20x = -24x
0 = (20 + -24x + 4x2)

Solving
0 = 20 + -24x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -20 = -20
-20 + 24x + -4x2 = 20 + -24x + 4x2 + -20 + 24x + -4x2

Reorder the terms:
-20 + 24x + -4x2 = 20 + -20 + -24x + 24x + 4x2 + -4x2

Combine like terms: 20 + -20 = 0
-20 + 24x + -4x2 = 0 + -24x + 24x + 4x2 + -4x2
-20 + 24x + -4x2 = -24x + 24x + 4x2 + -4x2

Combine like terms: -24x + 24x = 0
-20 + 24x + -4x2 = 0 + 4x2 + -4x2
-20 + 24x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-20 + 24x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 6x + -1x2) = 0

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {5, 1}