(2x^2-3x^3)-(9x^2-5x^3)=0

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Solution for (2x^2-3x^3)-(9x^2-5x^3)=0 equation: 


Simplifying
(2x2 + -3x3) + -1(9x2 + -5x3) = 0

Remove parenthesis around (2x2 + -3x3)
2x2 + -3x3 + -1(9x2 + -5x3) = 0
2x2 + -3x3 + (9x2 * -1 + -5x3 * -1) = 0
2x2 + -3x3 + (-9x2 + 5x3) = 0

Reorder the terms:
2x2 + -9x2 + -3x3 + 5x3 = 0

Combine like terms: 2x2 + -9x2 = -7x2
-7x2 + -3x3 + 5x3 = 0

Combine like terms: -3x3 + 5x3 = 2x3
-7x2 + 2x3 = 0

Solving
-7x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-7 + 2x) = 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 '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0, 3.5}

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