15000(100+x)(100+x)=21600

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Solution for 15000(100+x)(100+x)=21600 equation: 


Simplifying
15000(100 + x)(100 + x) = 21600

Multiply (100 + x) * (100 + x)
15000(100(100 + x) + x(100 + x)) = 21600
15000((100 * 100 + x * 100) + x(100 + x)) = 21600
15000((10000 + 100x) + x(100 + x)) = 21600
15000(10000 + 100x + (100 * x + x * x)) = 21600
15000(10000 + 100x + (100x + x2)) = 21600

Combine like terms: 100x + 100x = 200x
15000(10000 + 200x + x2) = 21600
(10000 * 15000 + 200x * 15000 + x2 * 15000) = 21600
(150000000 + 3000000x + 15000x2) = 21600

Solving
150000000 + 3000000x + 15000x2 = 21600

Solving for variable 'x'.

Reorder the terms:
150000000 + -21600 + 3000000x + 15000x2 = 21600 + -21600

Combine like terms: 150000000 + -21600 = 149978400
149978400 + 3000000x + 15000x2 = 21600 + -21600

Combine like terms: 21600 + -21600 = 0
149978400 + 3000000x + 15000x2 = 0

Factor out the Greatest Common Factor (GCF), '600'.
600(249964 + 5000x + 25x2) = 0

Factor a trinomial.
600((506 + 5x)(494 + 5x)) = 0

Ignore the factor 600.

Subproblem 1
Set the factor '(506 + 5x)' equal to zero and attempt to solve:

Simplifying
506 + 5x = 0

Solving
506 + 5x = 0

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

Add '-506' to each side of the equation.
506 + -506 + 5x = 0 + -506

Combine like terms: 506 + -506 = 0
0 + 5x = 0 + -506
5x = 0 + -506

Combine like terms: 0 + -506 = -506
5x = -506

Divide each side by '5'.
x = -101.2

Simplifying
x = -101.2

Subproblem 2
Set the factor '(494 + 5x)' equal to zero and attempt to solve:

Simplifying
494 + 5x = 0

Solving
494 + 5x = 0

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

Add '-494' to each side of the equation.
494 + -494 + 5x = 0 + -494

Combine like terms: 494 + -494 = 0
0 + 5x = 0 + -494
5x = 0 + -494

Combine like terms: 0 + -494 = -494
5x = -494

Divide each side by '5'.
x = -98.8

Simplifying
x = -98.8
Solution
x = {-101.2, -98.8}

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