y(2y+3)=5

Solution for y(2y+3)=5 equation:

Simplifying
y(2y + 3) = 5

Reorder the terms:
y(3 + 2y) = 5
(3 * y + 2y * y) = 5
(3y + 2y2) = 5

Solving
3y + 2y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + 3y + 2y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 3y + 2y2 = 0

Factor a trinomial.
(-5 + -2y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-5 + -2y)' equal to zero and attempt to solve:

Simplifying
-5 + -2y = 0

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

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

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

Divide each side by '-2'.
y = -2.5

Simplifying
y = -2.5
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1y = 0 + -1

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

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

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

Simplifying
y = 1
Solution
y = {-2.5, 1}