=2y^2-5y-12

Solution for =2y^2-5y-12 equation:

Simplifying
0 = 2y2 + -5y + -12

Reorder the terms:
0 = -12 + -5y + 2y2

Solving
0 = -12 + -5y + 2y2

Solving for variable 'y'.

Combine like terms: 0 + 12 = 12
12 + 5y + -2y2 = -12 + -5y + 2y2 + 12 + 5y + -2y2

Reorder the terms:
12 + 5y + -2y2 = -12 + 12 + -5y + 5y + 2y2 + -2y2

Combine like terms: -12 + 12 = 0
12 + 5y + -2y2 = 0 + -5y + 5y + 2y2 + -2y2
12 + 5y + -2y2 = -5y + 5y + 2y2 + -2y2

Combine like terms: -5y + 5y = 0
12 + 5y + -2y2 = 0 + 2y2 + -2y2
12 + 5y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
12 + 5y + -2y2 = 0

Factor a trinomial.
(4 + -1y)(3 + 2y) = 0

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

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

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

Simplifying
3 + 2y = 0

Solving
3 + 2y = 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 + 2y = 0 + -3

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

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

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {4, -1.5}