(x-5)(4x-4)=-16

Solution for (x-5)(4x-4)=-16 equation:

Simplifying
(x + -5)(4x + -4) = -16

Reorder the terms:
(-5 + x)(4x + -4) = -16

Reorder the terms:
(-5 + x)(-4 + 4x) = -16

Multiply (-5 + x) * (-4 + 4x)
(-5(-4 + 4x) + x(-4 + 4x)) = -16
((-4 * -5 + 4x * -5) + x(-4 + 4x)) = -16
((20 + -20x) + x(-4 + 4x)) = -16
(20 + -20x + (-4 * x + 4x * x)) = -16
(20 + -20x + (-4x + 4x2)) = -16

Combine like terms: -20x + -4x = -24x
(20 + -24x + 4x2) = -16

Solving
20 + -24x + 4x2 = -16

Solving for variable 'x'.

Reorder the terms:
20 + 16 + -24x + 4x2 = -16 + 16

Combine like terms: 20 + 16 = 36
36 + -24x + 4x2 = -16 + 16

Combine like terms: -16 + 16 = 0
36 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -6x + x2) = 0

Factor a trinomial.
4((3 + -1x)(3 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}