(13-2x)(16-2x)=108

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Solution for (13-2x)(16-2x)=108 equation: 


Simplifying
(13 + -2x)(16 + -2x) = 108

Multiply (13 + -2x) * (16 + -2x)
(13(16 + -2x) + -2x * (16 + -2x)) = 108
((16 * 13 + -2x * 13) + -2x * (16 + -2x)) = 108
((208 + -26x) + -2x * (16 + -2x)) = 108
(208 + -26x + (16 * -2x + -2x * -2x)) = 108
(208 + -26x + (-32x + 4x2)) = 108

Combine like terms: -26x + -32x = -58x
(208 + -58x + 4x2) = 108

Solving
208 + -58x + 4x2 = 108

Solving for variable 'x'.

Reorder the terms:
208 + -108 + -58x + 4x2 = 108 + -108

Combine like terms: 208 + -108 = 100
100 + -58x + 4x2 = 108 + -108

Combine like terms: 108 + -108 = 0
100 + -58x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(50 + -29x + 2x2) = 0

Factor a trinomial.
2((2 + -1x)(25 + -2x)) = 0

Ignore the factor 2.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(25 + -2x)' equal to zero and attempt to solve:

Simplifying
25 + -2x = 0

Solving
25 + -2x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -2x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -2x = 0 + -25
-2x = 0 + -25

Combine like terms: 0 + -25 = -25
-2x = -25

Divide each side by '-2'.
x = 12.5

Simplifying
x = 12.5
Solution
x = {2, 12.5}

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