12y^2+7y-10=0

Solution for 12y^2+7y-10=0 equation:

Simplifying
12y2 + 7y + -10 = 0

Reorder the terms:
-10 + 7y + 12y2 = 0

Solving
-10 + 7y + 12y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-5 + -4y)(2 + -3y) = 0

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

Simplifying
-5 + -4y = 0

Solving
-5 + -4y = 0

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

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

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

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

Divide each side by '-4'.
y = -1.25

Simplifying
y = -1.25
Subproblem 2
Set the factor '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 0

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

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

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

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

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {-1.25, 0.6666666667}