3x(3x^2-4x)=2x(2x^2+5x)

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Solution for 3x(3x^2-4x)=2x(2x^2+5x) equation: 


Simplifying
3x(3x2 + -4x) = 2x(2x2 + 5x)

Reorder the terms:
3x(-4x + 3x2) = 2x(2x2 + 5x)
(-4x * 3x + 3x2 * 3x) = 2x(2x2 + 5x)
(-12x2 + 9x3) = 2x(2x2 + 5x)

Reorder the terms:
-12x2 + 9x3 = 2x(5x + 2x2)
-12x2 + 9x3 = (5x * 2x + 2x2 * 2x)
-12x2 + 9x3 = (10x2 + 4x3)

Solving
-12x2 + 9x3 = 10x2 + 4x3

Solving for variable 'x'.

Reorder the terms:
-12x2 + -10x2 + 9x3 + -4x3 = 10x2 + 4x3 + -10x2 + -4x3

Combine like terms: -12x2 + -10x2 = -22x2
-22x2 + 9x3 + -4x3 = 10x2 + 4x3 + -10x2 + -4x3

Combine like terms: 9x3 + -4x3 = 5x3
-22x2 + 5x3 = 10x2 + 4x3 + -10x2 + -4x3

Reorder the terms:
-22x2 + 5x3 = 10x2 + -10x2 + 4x3 + -4x3

Combine like terms: 10x2 + -10x2 = 0
-22x2 + 5x3 = 0 + 4x3 + -4x3
-22x2 + 5x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-22x2 + 5x3 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-22 + 5x) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-22 + 5x)' equal to zero and attempt to solve:

Simplifying
-22 + 5x = 0

Solving
-22 + 5x = 0

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

Add '22' to each side of the equation.
-22 + 22 + 5x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 5x = 0 + 22
5x = 0 + 22

Combine like terms: 0 + 22 = 22
5x = 22

Divide each side by '5'.
x = 4.4

Simplifying
x = 4.4
Solution
x = {0, 4.4}

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