(60-2x)(80-2x)=1500

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Solution for (60-2x)(80-2x)=1500 equation: 


Simplifying
(60 + -2x)(80 + -2x) = 1500

Multiply (60 + -2x) * (80 + -2x)
(60(80 + -2x) + -2x * (80 + -2x)) = 1500
((80 * 60 + -2x * 60) + -2x * (80 + -2x)) = 1500
((4800 + -120x) + -2x * (80 + -2x)) = 1500
(4800 + -120x + (80 * -2x + -2x * -2x)) = 1500
(4800 + -120x + (-160x + 4x2)) = 1500

Combine like terms: -120x + -160x = -280x
(4800 + -280x + 4x2) = 1500

Solving
4800 + -280x + 4x2 = 1500

Solving for variable 'x'.

Reorder the terms:
4800 + -1500 + -280x + 4x2 = 1500 + -1500

Combine like terms: 4800 + -1500 = 3300
3300 + -280x + 4x2 = 1500 + -1500

Combine like terms: 1500 + -1500 = 0
3300 + -280x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(825 + -70x + x2) = 0

Factor a trinomial.
4((15 + -1x)(55 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15

Subproblem 2
Set the factor '(55 + -1x)' equal to zero and attempt to solve:

Simplifying
55 + -1x = 0

Solving
55 + -1x = 0

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

Add '-55' to each side of the equation.
55 + -55 + -1x = 0 + -55

Combine like terms: 55 + -55 = 0
0 + -1x = 0 + -55
-1x = 0 + -55

Combine like terms: 0 + -55 = -55
-1x = -55

Divide each side by '-1'.
x = 55

Simplifying
x = 55
Solution
x = {15, 55}

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