(6x^2-3x^3)-(8x^2-8x^3)=0

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Solution for (6x^2-3x^3)-(8x^2-8x^3)=0 equation: 


Simplifying
(6x2 + -3x3) + -1(8x2 + -8x3) = 0

Remove parenthesis around (6x2 + -3x3)
6x2 + -3x3 + -1(8x2 + -8x3) = 0
6x2 + -3x3 + (8x2 * -1 + -8x3 * -1) = 0
6x2 + -3x3 + (-8x2 + 8x3) = 0

Reorder the terms:
6x2 + -8x2 + -3x3 + 8x3 = 0

Combine like terms: 6x2 + -8x2 = -2x2
-2x2 + -3x3 + 8x3 = 0

Combine like terms: -3x3 + 8x3 = 5x3
-2x2 + 5x3 = 0

Solving
-2x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-2 + 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 '(-2 + 5x)' equal to zero and attempt to solve:

Simplifying
-2 + 5x = 0

Solving
-2 + 5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + 5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5x = 0 + 2
5x = 0 + 2

Combine like terms: 0 + 2 = 2
5x = 2

Divide each side by '5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {0, 0.4}

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