(26-2x)(16-2x)=200

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Solution for (26-2x)(16-2x)=200 equation: 


Simplifying
(26 + -2x)(16 + -2x) = 200

Multiply (26 + -2x) * (16 + -2x)
(26(16 + -2x) + -2x * (16 + -2x)) = 200
((16 * 26 + -2x * 26) + -2x * (16 + -2x)) = 200
((416 + -52x) + -2x * (16 + -2x)) = 200
(416 + -52x + (16 * -2x + -2x * -2x)) = 200
(416 + -52x + (-32x + 4x2)) = 200

Combine like terms: -52x + -32x = -84x
(416 + -84x + 4x2) = 200

Solving
416 + -84x + 4x2 = 200

Solving for variable 'x'.

Reorder the terms:
416 + -200 + -84x + 4x2 = 200 + -200

Combine like terms: 416 + -200 = 216
216 + -84x + 4x2 = 200 + -200

Combine like terms: 200 + -200 = 0
216 + -84x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(54 + -21x + x2) = 0

Factor a trinomial.
4((3 + -1x)(18 + -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 '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {3, 18}

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