150(100+x)(100+x)=21600

Solution for 150(100+x)(100+x)=21600 equation:

Simplifying
150(100 + x)(100 + x) = 21600

Multiply (100 + x) * (100 + x)
150(100(100 + x) + x(100 + x)) = 21600
150((100 * 100 + x * 100) + x(100 + x)) = 21600
150((10000 + 100x) + x(100 + x)) = 21600
150(10000 + 100x + (100 * x + x * x)) = 21600
150(10000 + 100x + (100x + x2)) = 21600

Combine like terms: 100x + 100x = 200x
150(10000 + 200x + x2) = 21600
(10000 * 150 + 200x * 150 + x2 * 150) = 21600
(1500000 + 30000x + 150x2) = 21600

Solving
1500000 + 30000x + 150x2 = 21600

Solving for variable 'x'.

Reorder the terms:
1500000 + -21600 + 30000x + 150x2 = 21600 + -21600

Combine like terms: 1500000 + -21600 = 1478400
1478400 + 30000x + 150x2 = 21600 + -21600

Combine like terms: 21600 + -21600 = 0
1478400 + 30000x + 150x2 = 0

Factor out the Greatest Common Factor (GCF), '150'.
150(9856 + 200x + x2) = 0

Factor a trinomial.
150((112 + x)(88 + x)) = 0

Ignore the factor 150.
Subproblem 1
Set the factor '(112 + x)' equal to zero and attempt to solve:

Simplifying
112 + x = 0

Solving
112 + x = 0

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

Add '-112' to each side of the equation.
112 + -112 + x = 0 + -112

Combine like terms: 112 + -112 = 0
0 + x = 0 + -112
x = 0 + -112

Combine like terms: 0 + -112 = -112
x = -112

Simplifying
x = -112
Subproblem 2
Set the factor '(88 + x)' equal to zero and attempt to solve:

Simplifying
88 + x = 0

Solving
88 + x = 0

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

Add '-88' to each side of the equation.
88 + -88 + x = 0 + -88

Combine like terms: 88 + -88 = 0
0 + x = 0 + -88
x = 0 + -88

Combine like terms: 0 + -88 = -88
x = -88

Simplifying
x = -88
Solution
x = {-112, -88}