y(2y+5)=12

Solution for y(2y+5)=12 equation:

Simplifying
y(2y + 5) = 12

Reorder the terms:
y(5 + 2y) = 12
(5 * y + 2y * y) = 12
(5y + 2y2) = 12

Solving
5y + 2y2 = 12

Solving for variable 'y'.

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

Combine like terms: 12 + -12 = 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}