4y^2+51y+162=0

Solution for 4y^2+51y+162=0 equation:

Simplifying
4y2 + 51y + 162 = 0

Reorder the terms:
162 + 51y + 4y2 = 0

Solving
162 + 51y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(27 + 4y)(6 + y) = 0

Subproblem 1
Set the factor '(27 + 4y)' equal to zero and attempt to solve:

Simplifying
27 + 4y = 0

Solving
27 + 4y = 0

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

Add '-27' to each side of the equation.
27 + -27 + 4y = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 4y = 0 + -27
4y = 0 + -27

Combine like terms: 0 + -27 = -27
4y = -27

Divide each side by '4'.
y = -6.75

Simplifying
y = -6.75
Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Solution
y = {-6.75, -6}