10x^3-3x=13x^2

Solution for 10x^3-3x=13x^2 equation:

Simplifying
10x3 + -3x = 13x2

Reorder the terms:
-3x + 10x3 = 13x2

Solving
-3x + 10x3 = 13x2

Solving for variable 'x'.

Reorder the terms:
-3x + -13x2 + 10x3 = 13x2 + -13x2

Combine like terms: 13x2 + -13x2 = 0
-3x + -13x2 + 10x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + -13x + 10x2) = 0

Factor a trinomial.
x((-1 + -5x)(3 + -2x)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 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 + -5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1

Combine like terms: 0 + 1 = 1
-5x = 1

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2
Subproblem 3
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, -0.2, 1.5}