(26-2x)(23-2x)=208

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Solution for (26-2x)(23-2x)=208 equation: 


Simplifying
(26 + -2x)(23 + -2x) = 208

Multiply (26 + -2x) * (23 + -2x)
(26(23 + -2x) + -2x * (23 + -2x)) = 208
((23 * 26 + -2x * 26) + -2x * (23 + -2x)) = 208
((598 + -52x) + -2x * (23 + -2x)) = 208
(598 + -52x + (23 * -2x + -2x * -2x)) = 208
(598 + -52x + (-46x + 4x2)) = 208

Combine like terms: -52x + -46x = -98x
(598 + -98x + 4x2) = 208

Solving
598 + -98x + 4x2 = 208

Solving for variable 'x'.

Reorder the terms:
598 + -208 + -98x + 4x2 = 208 + -208

Combine like terms: 598 + -208 = 390
390 + -98x + 4x2 = 208 + -208

Combine like terms: 208 + -208 = 0
390 + -98x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(195 + -49x + 2x2) = 0

Factor a trinomial.
2((5 + -1x)(39 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(39 + -2x)' equal to zero and attempt to solve:

Simplifying
39 + -2x = 0

Solving
39 + -2x = 0

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

Add '-39' to each side of the equation.
39 + -39 + -2x = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -2x = 0 + -39
-2x = 0 + -39

Combine like terms: 0 + -39 = -39
-2x = -39

Divide each side by '-2'.
x = 19.5

Simplifying
x = 19.5
Solution
x = {5, 19.5}

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