4y^2+3y-76=0

Solution for 4y^2+3y-76=0 equation:

Simplifying
4y2 + 3y + -76 = 0

Reorder the terms:
-76 + 3y + 4y2 = 0

Solving
-76 + 3y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-19 + -4y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-19 + -4y)' equal to zero and attempt to solve:

Simplifying
-19 + -4y = 0

Solving
-19 + -4y = 0

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

Add '19' to each side of the equation.
-19 + 19 + -4y = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -4y = 0 + 19
-4y = 0 + 19

Combine like terms: 0 + 19 = 19
-4y = 19

Divide each side by '-4'.
y = -4.75

Simplifying
y = -4.75
Subproblem 2
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
Solution
y = {-4.75, 4}