0=6x^3+5x^2

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Solution for 0=6x^3+5x^2 equation: 


Simplifying
0 = 6x3 + 5x2

Reorder the terms:
0 = 5x2 + 6x3

Solving
0 = 5x2 + 6x3

Solving for variable 'x'.
Remove the zero:
-5x2 + -6x3 = 5x2 + 6x3 + -5x2 + -6x3

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

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

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

Factor out the Greatest Common Factor (GCF), '-1x2'.
-1x2(5 + 6x) = 0

Ignore the factor -1.

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 '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Solution
x = {0, -0.8333333333}

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