(84-2x)(60-2x)=880

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Solution for (84-2x)(60-2x)=880 equation:


Simplifying
(84 + -2x)(60 + -2x) = 880

Multiply (84 + -2x) * (60 + -2x)
(84(60 + -2x) + -2x * (60 + -2x)) = 880
((60 * 84 + -2x * 84) + -2x * (60 + -2x)) = 880
((5040 + -168x) + -2x * (60 + -2x)) = 880
(5040 + -168x + (60 * -2x + -2x * -2x)) = 880
(5040 + -168x + (-120x + 4x2)) = 880

Combine like terms: -168x + -120x = -288x
(5040 + -288x + 4x2) = 880

Solving
5040 + -288x + 4x2 = 880

Solving for variable 'x'.

Reorder the terms:
5040 + -880 + -288x + 4x2 = 880 + -880

Combine like terms: 5040 + -880 = 4160
4160 + -288x + 4x2 = 880 + -880

Combine like terms: 880 + -880 = 0
4160 + -288x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1040 + -72x + x2) = 0

Factor a trinomial.
4((20 + -1x)(52 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20

Subproblem 2
Set the factor '(52 + -1x)' equal to zero and attempt to solve:

Simplifying
52 + -1x = 0

Solving
52 + -1x = 0

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

Add '-52' to each side of the equation.
52 + -52 + -1x = 0 + -52

Combine like terms: 52 + -52 = 0
0 + -1x = 0 + -52
-1x = 0 + -52

Combine like terms: 0 + -52 = -52
-1x = -52

Divide each side by '-1'.
x = 52

Simplifying
x = 52
Solution
x = {20, 52}

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