12y^2+5y-3=0

Solution for 12y^2+5y-3=0 equation:

Simplifying
12y2 + 5y + -3 = 0

Reorder the terms:
-3 + 5y + 12y2 = 0

Solving
-3 + 5y + 12y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -4y)(1 + -3y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -3y)' equal to zero and attempt to solve:

Simplifying
1 + -3y = 0

Solving
1 + -3y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3y = 0 + -1
-3y = 0 + -1

Combine like terms: 0 + -1 = -1
-3y = -1

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Solution
y = {-0.75, 0.3333333333}