(8x^2-5x^3)-(6x^2-8x^3)=0

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Solution for (8x^2-5x^3)-(6x^2-8x^3)=0 equation: 


Simplifying
(8x2 + -5x3) + -1(6x2 + -8x3) = 0

Remove parenthesis around (8x2 + -5x3)
8x2 + -5x3 + -1(6x2 + -8x3) = 0
8x2 + -5x3 + (6x2 * -1 + -8x3 * -1) = 0
8x2 + -5x3 + (-6x2 + 8x3) = 0

Reorder the terms:
8x2 + -6x2 + -5x3 + 8x3 = 0

Combine like terms: 8x2 + -6x2 = 2x2
2x2 + -5x3 + 8x3 = 0

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

Solving
2x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(2 + 3x) = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, -0.6666666667}

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