80=(4-4x)(10-4x)

Solution for 80=(4-4x)(10-4x) equation:

Simplifying
80 = (4 + -4x)(10 + -4x)

Multiply (4 + -4x) * (10 + -4x)
80 = (4(10 + -4x) + -4x * (10 + -4x))
80 = ((10 * 4 + -4x * 4) + -4x * (10 + -4x))
80 = ((40 + -16x) + -4x * (10 + -4x))
80 = (40 + -16x + (10 * -4x + -4x * -4x))
80 = (40 + -16x + (-40x + 16x2))

Combine like terms: -16x + -40x = -56x
80 = (40 + -56x + 16x2)

Solving
80 = 40 + -56x + 16x2

Solving for variable 'x'.

Combine like terms: 80 + -40 = 40
40 + 56x + -16x2 = 40 + -56x + 16x2 + -40 + 56x + -16x2

Reorder the terms:
40 + 56x + -16x2 = 40 + -40 + -56x + 56x + 16x2 + -16x2

Combine like terms: 40 + -40 = 0
40 + 56x + -16x2 = 0 + -56x + 56x + 16x2 + -16x2
40 + 56x + -16x2 = -56x + 56x + 16x2 + -16x2

Combine like terms: -56x + 56x = 0
40 + 56x + -16x2 = 0 + 16x2 + -16x2
40 + 56x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
40 + 56x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + 7x + -2x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(5 + 7x + -2x2)' equal to zero and attempt to solve:

Simplifying
5 + 7x + -2x2 = 0

Solving
5 + 7x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-2.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -3.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -3.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -3.5x + x2 = 0 + 2.5
-3.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-3.5x + x2 = 2.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 2.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 2.5 + 3.0625

Combine like terms: 2.5 + 3.0625 = 5.5625
3.0625 + -3.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.358495283 and -2.358495283.

Subproblem 1
x + -1.75 = 2.358495283

Simplifying
x + -1.75 = 2.358495283

Reorder the terms:
-1.75 + x = 2.358495283

Solving
-1.75 + x = 2.358495283

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 2.358495283 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.358495283 + 1.75
x = 2.358495283 + 1.75

Combine like terms: 2.358495283 + 1.75 = 4.108495283
x = 4.108495283

Simplifying
x = 4.108495283

Subproblem 2
x + -1.75 = -2.358495283

Simplifying
x + -1.75 = -2.358495283

Reorder the terms:
-1.75 + x = -2.358495283

Solving
-1.75 + x = -2.358495283

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -2.358495283 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.358495283 + 1.75
x = -2.358495283 + 1.75

Combine like terms: -2.358495283 + 1.75 = -0.608495283
x = -0.608495283

Simplifying
x = -0.608495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.108495283, -0.608495283}
Solution
x = {4.108495283, -0.608495283}