(4x^2-3x^3)-(6x^2-9x^3)=0

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Solution for (4x^2-3x^3)-(6x^2-9x^3)=0 equation:


Simplifying
(4x2 + -3x3) + -1(6x2 + -9x3) = 0

Remove parenthesis around (4x2 + -3x3)
4x2 + -3x3 + -1(6x2 + -9x3) = 0
4x2 + -3x3 + (6x2 * -1 + -9x3 * -1) = 0
4x2 + -3x3 + (-6x2 + 9x3) = 0

Reorder the terms:
4x2 + -6x2 + -3x3 + 9x3 = 0

Combine like terms: 4x2 + -6x2 = -2x2
-2x2 + -3x3 + 9x3 = 0

Combine like terms: -3x3 + 9x3 = 6x3
-2x2 + 6x3 = 0

Solving
-2x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-1 + 3x) = 0

Ignore the factor 2.

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 '(-1 + 3x)' equal to zero and attempt to solve: Simplifying -1 + 3x = 0 Solving -1 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3x = 0 + 1 3x = 0 + 1 Combine like terms: 0 + 1 = 1 3x = 1 Divide each side by '3'. x = 0.3333333333 Simplifying x = 0.3333333333

Solution

x = {0, 0.3333333333}

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