(80-2x)(40-2x)=1904

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Solution for (80-2x)(40-2x)=1904 equation: 


Simplifying
(80 + -2x)(40 + -2x) = 1904

Multiply (80 + -2x) * (40 + -2x)
(80(40 + -2x) + -2x * (40 + -2x)) = 1904
((40 * 80 + -2x * 80) + -2x * (40 + -2x)) = 1904
((3200 + -160x) + -2x * (40 + -2x)) = 1904
(3200 + -160x + (40 * -2x + -2x * -2x)) = 1904
(3200 + -160x + (-80x + 4x2)) = 1904

Combine like terms: -160x + -80x = -240x
(3200 + -240x + 4x2) = 1904

Solving
3200 + -240x + 4x2 = 1904

Solving for variable 'x'.

Reorder the terms:
3200 + -1904 + -240x + 4x2 = 1904 + -1904

Combine like terms: 3200 + -1904 = 1296
1296 + -240x + 4x2 = 1904 + -1904

Combine like terms: 1904 + -1904 = 0
1296 + -240x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(324 + -60x + x2) = 0

Factor a trinomial.
4((6 + -1x)(54 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(54 + -1x)' equal to zero and attempt to solve:

Simplifying
54 + -1x = 0

Solving
54 + -1x = 0

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

Add '-54' to each side of the equation.
54 + -54 + -1x = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -1x = 0 + -54
-1x = 0 + -54

Combine like terms: 0 + -54 = -54
-1x = -54

Divide each side by '-1'.
x = 54

Simplifying
x = 54
Solution
x = {6, 54}

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