(60-2x)(60-2x)-60x=0

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Solution for (60-2x)(60-2x)-60x=0 equation: 


Simplifying
(60 + -2x)(60 + -2x) + -60x = 0

Multiply (60 + -2x) * (60 + -2x)
(60(60 + -2x) + -2x * (60 + -2x)) + -60x = 0
((60 * 60 + -2x * 60) + -2x * (60 + -2x)) + -60x = 0
((3600 + -120x) + -2x * (60 + -2x)) + -60x = 0
(3600 + -120x + (60 * -2x + -2x * -2x)) + -60x = 0
(3600 + -120x + (-120x + 4x2)) + -60x = 0

Combine like terms: -120x + -120x = -240x
(3600 + -240x + 4x2) + -60x = 0

Reorder the terms:
3600 + -240x + -60x + 4x2 = 0

Combine like terms: -240x + -60x = -300x
3600 + -300x + 4x2 = 0

Solving
3600 + -300x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(900 + -75x + x2) = 0

Factor a trinomial.
4((15 + -1x)(60 + -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 '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Solution
x = {15, 60}

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