(60-2x)(80-2x)=800

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Solution for (60-2x)(80-2x)=800 equation:


Simplifying
(60 + -2x)(80 + -2x) = 800

Multiply (60 + -2x) * (80 + -2x)
(60(80 + -2x) + -2x * (80 + -2x)) = 800
((80 * 60 + -2x * 60) + -2x * (80 + -2x)) = 800
((4800 + -120x) + -2x * (80 + -2x)) = 800
(4800 + -120x + (80 * -2x + -2x * -2x)) = 800
(4800 + -120x + (-160x + 4x2)) = 800

Combine like terms: -120x + -160x = -280x
(4800 + -280x + 4x2) = 800

Solving
4800 + -280x + 4x2 = 800

Solving for variable 'x'.

Reorder the terms:
4800 + -800 + -280x + 4x2 = 800 + -800

Combine like terms: 4800 + -800 = 4000
4000 + -280x + 4x2 = 800 + -800

Combine like terms: 800 + -800 = 0
4000 + -280x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1000 + -70x + x2) = 0

Factor a trinomial.
4((20 + -1x)(50 + -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 '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x = 0 + -50
-1x = 0 + -50

Combine like terms: 0 + -50 = -50
-1x = -50

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Solution
x = {20, 50}

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