(10-2x)(8-2x)=8

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Solution for (10-2x)(8-2x)=8 equation: 


Simplifying
(10 + -2x)(8 + -2x) = 8

Multiply (10 + -2x) * (8 + -2x)
(10(8 + -2x) + -2x * (8 + -2x)) = 8
((8 * 10 + -2x * 10) + -2x * (8 + -2x)) = 8
((80 + -20x) + -2x * (8 + -2x)) = 8
(80 + -20x + (8 * -2x + -2x * -2x)) = 8
(80 + -20x + (-16x + 4x2)) = 8

Combine like terms: -20x + -16x = -36x
(80 + -36x + 4x2) = 8

Solving
80 + -36x + 4x2 = 8

Solving for variable 'x'.

Reorder the terms:
80 + -8 + -36x + 4x2 = 8 + -8

Combine like terms: 80 + -8 = 72
72 + -36x + 4x2 = 8 + -8

Combine like terms: 8 + -8 = 0
72 + -36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -9x + x2) = 0

Factor a trinomial.
4((3 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {3, 6}

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