(40-2x)(18-2x)-408=0

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Solution for (40-2x)(18-2x)-408=0 equation: 


Simplifying
(40 + -2x)(18 + -2x) + -408 = 0

Multiply (40 + -2x) * (18 + -2x)
(40(18 + -2x) + -2x * (18 + -2x)) + -408 = 0
((18 * 40 + -2x * 40) + -2x * (18 + -2x)) + -408 = 0
((720 + -80x) + -2x * (18 + -2x)) + -408 = 0
(720 + -80x + (18 * -2x + -2x * -2x)) + -408 = 0
(720 + -80x + (-36x + 4x2)) + -408 = 0

Combine like terms: -80x + -36x = -116x
(720 + -116x + 4x2) + -408 = 0

Reorder the terms:
720 + -408 + -116x + 4x2 = 0

Combine like terms: 720 + -408 = 312
312 + -116x + 4x2 = 0

Solving
312 + -116x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(78 + -29x + x2) = 0

Factor a trinomial.
4((3 + -1x)(26 + -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 '(26 + -1x)' equal to zero and attempt to solve:

Simplifying
26 + -1x = 0

Solving
26 + -1x = 0

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

Add '-26' to each side of the equation.
26 + -26 + -1x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -1x = 0 + -26
-1x = 0 + -26

Combine like terms: 0 + -26 = -26
-1x = -26

Divide each side by '-1'.
x = 26

Simplifying
x = 26
Solution
x = {3, 26}

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