6y+120y^2-72=0

Solution for 6y+120y^2-72=0 equation:

Simplifying
6y + 120y2 + -72 = 0

Reorder the terms:
-72 + 6y + 120y2 = 0

Solving
-72 + 6y + 120y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + y + 20y2) = 0

Factor a trinomial.
6((-4 + -5y)(3 + -4y)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-4 + -5y)' equal to zero and attempt to solve:

Simplifying
-4 + -5y = 0

Solving
-4 + -5y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5y = 0 + 4
-5y = 0 + 4

Combine like terms: 0 + 4 = 4
-5y = 4

Divide each side by '-5'.
y = -0.8

Simplifying
y = -0.8
Subproblem 2
Set the factor '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3

Combine like terms: 0 + -3 = -3
-4y = -3

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
Solution
y = {-0.8, 0.75}