x[x-15]=3x[108-5x]

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Solution for x[x-15]=3x[108-5x] equation: 


Simplifying
x[x + -15] = 3x[108 + -5x]

Reorder the terms:
x[-15 + x] = 3x[108 + -5x]
[-15 * x + x * x] = 3x[108 + -5x]
[-15x + x2] = 3x[108 + -5x]
-15x + x2 = [108 * 3x + -5x * 3x]
-15x + x2 = [324x + -15x2]

Solving
-15x + x2 = 324x + -15x2

Solving for variable 'x'.

Reorder the terms:
-15x + -324x + x2 + 15x2 = 324x + -15x2 + -324x + 15x2

Combine like terms: -15x + -324x = -339x
-339x + x2 + 15x2 = 324x + -15x2 + -324x + 15x2

Combine like terms: x2 + 15x2 = 16x2
-339x + 16x2 = 324x + -15x2 + -324x + 15x2

Reorder the terms:
-339x + 16x2 = 324x + -324x + -15x2 + 15x2

Combine like terms: 324x + -324x = 0
-339x + 16x2 = 0 + -15x2 + 15x2
-339x + 16x2 = -15x2 + 15x2

Combine like terms: -15x2 + 15x2 = 0
-339x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-339 + 16x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-339 + 16x)' equal to zero and attempt to solve:

Simplifying
-339 + 16x = 0

Solving
-339 + 16x = 0

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

Add '339' to each side of the equation.
-339 + 339 + 16x = 0 + 339

Combine like terms: -339 + 339 = 0
0 + 16x = 0 + 339
16x = 0 + 339

Combine like terms: 0 + 339 = 339
16x = 339

Divide each side by '16'.
x = 21.1875

Simplifying
x = 21.1875
Solution
x = {0, 21.1875}

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