(10-2x)(12-2x)=80

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Solution for (10-2x)(12-2x)=80 equation: 


Simplifying
(10 + -2x)(12 + -2x) = 80

Multiply (10 + -2x) * (12 + -2x)
(10(12 + -2x) + -2x * (12 + -2x)) = 80
((12 * 10 + -2x * 10) + -2x * (12 + -2x)) = 80
((120 + -20x) + -2x * (12 + -2x)) = 80
(120 + -20x + (12 * -2x + -2x * -2x)) = 80
(120 + -20x + (-24x + 4x2)) = 80

Combine like terms: -20x + -24x = -44x
(120 + -44x + 4x2) = 80

Solving
120 + -44x + 4x2 = 80

Solving for variable 'x'.

Reorder the terms:
120 + -80 + -44x + 4x2 = 80 + -80

Combine like terms: 120 + -80 = 40
40 + -44x + 4x2 = 80 + -80

Combine like terms: 80 + -80 = 0
40 + -44x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + -11x + x2) = 0

Factor a trinomial.
4((1 + -1x)(10 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {1, 10}

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