150((100(100+x))(100(100+x)))=216

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Solution for 150((100(100+x))(100(100+x)))=216 equation: 


Simplifying
150((100(100 + x))(100(100 + x))) = 216
150(((100 * 100 + x * 100))(100(100 + x))) = 216
150(((10000 + 100x))(100(100 + x))) = 216
150((10000 + 100x)((100 * 100 + x * 100))) = 216
150((10000 + 100x)((10000 + 100x))) = 216

Multiply (10000 + 100x) * (10000 + 100x)
150((10000(10000 + 100x) + 100x * (10000 + 100x))) = 216
150(((10000 * 10000 + 100x * 10000) + 100x * (10000 + 100x))) = 216
150(((100000000 + 1000000x) + 100x * (10000 + 100x))) = 216
150((100000000 + 1000000x + (10000 * 100x + 100x * 100x))) = 216
150((100000000 + 1000000x + (1000000x + 10000x2))) = 216

Combine like terms: 1000000x + 1000000x = 2000000x
150((100000000 + 2000000x + 10000x2)) = 216
(100000000 * 150 + 2000000x * 150 + 10000x2 * 150) = 216
(15000000000 + 300000000x + 1500000x2) = 216

Solving
15000000000 + 300000000x + 1500000x2 = 216

Solving for variable 'x'.

Reorder the terms:
15000000000 + -216 + 300000000x + 1500000x2 = 216 + -216

Combine like terms: 15000000000 + -216 = 14999999784
14999999784 + 300000000x + 1500000x2 = 216 + -216

Combine like terms: 216 + -216 = 0
14999999784 + 300000000x + 1500000x2 = 0

Factor out the Greatest Common Factor (GCF), '24'.
24(624999991 + 12500000x + 62500x2) = 0

Factor a trinomial.
24((25003 + 250x)(24997 + 250x)) = 0

Ignore the factor 24.

Subproblem 1
Set the factor '(25003 + 250x)' equal to zero and attempt to solve:

Simplifying
25003 + 250x = 0

Solving
25003 + 250x = 0

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

Add '-25003' to each side of the equation.
25003 + -25003 + 250x = 0 + -25003

Combine like terms: 25003 + -25003 = 0
0 + 250x = 0 + -25003
250x = 0 + -25003

Combine like terms: 0 + -25003 = -25003
250x = -25003

Divide each side by '250'.
x = -100.012

Simplifying
x = -100.012

Subproblem 2
Set the factor '(24997 + 250x)' equal to zero and attempt to solve:

Simplifying
24997 + 250x = 0

Solving
24997 + 250x = 0

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

Add '-24997' to each side of the equation.
24997 + -24997 + 250x = 0 + -24997

Combine like terms: 24997 + -24997 = 0
0 + 250x = 0 + -24997
250x = 0 + -24997

Combine like terms: 0 + -24997 = -24997
250x = -24997

Divide each side by '250'.
x = -99.988

Simplifying
x = -99.988
Solution
x = {-100.012, -99.988}

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