5y^3-126y=9y^2

Solution for 5y^3-126y=9y^2 equation:

Simplifying
5y3 + -126y = 9y2

Reorder the terms:
-126y + 5y3 = 9y2

Solving
-126y + 5y3 = 9y2

Solving for variable 'y'.

Reorder the terms:
-126y + -9y2 + 5y3 = 9y2 + -9y2

Combine like terms: 9y2 + -9y2 = 0
-126y + -9y2 + 5y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-126 + -9y + 5y2) = 0

Factor a trinomial.
y((-21 + -5y)(6 + -1y)) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-21 + -5y)' equal to zero and attempt to solve:

Simplifying
-21 + -5y = 0

Solving
-21 + -5y = 0

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

Add '21' to each side of the equation.
-21 + 21 + -5y = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -5y = 0 + 21
-5y = 0 + 21

Combine like terms: 0 + 21 = 21
-5y = 21

Divide each side by '-5'.
y = -4.2

Simplifying
y = -4.2
Subproblem 3
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

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

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

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

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

Simplifying
y = 6
Solution
y = {0, -4.2, 6}