2x(60-2x)-400=100

Solution for 2x(60-2x)-400=100 equation:

Simplifying
2x(60 + -2x) + -400 = 100
(60 * 2x + -2x * 2x) + -400 = 100
(120x + -4x2) + -400 = 100

Reorder the terms:
-400 + 120x + -4x2 = 100

Solving
-400 + 120x + -4x2 = 100

Solving for variable 'x'.

Reorder the terms:
-400 + -100 + 120x + -4x2 = 100 + -100

Combine like terms: -400 + -100 = -500
-500 + 120x + -4x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-500 + 120x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-125 + 30x + -1x2) = 0

Factor a trinomial.
4((-25 + x)(5 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-25 + x)' equal to zero and attempt to solve:

Simplifying
-25 + x = 0

Solving
-25 + x = 0

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

Add '25' to each side of the equation.
-25 + 25 + x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + x = 0 + 25
x = 0 + 25

Combine like terms: 0 + 25 = 25
x = 25

Simplifying
x = 25
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {25, 5}