2x^2+60x=2x^3

Solution for 2x^2+60x=2x^3 equation:

Simplifying
2x2 + 60x = 2x3

Reorder the terms:
60x + 2x2 = 2x3

Solving
60x + 2x2 = 2x3

Solving for variable 'x'.

Combine like terms: 2x3 + -2x3 = 0
60x + 2x2 + -2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(30 + x + -1x2) = 0

Factor a trinomial.
2x((6 + -1x)(5 + x)) = 0

Ignore the factor 2.
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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 3
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5
Solution
x = {0, 6, -5}