(2y+3)(2y-1)=5

Solution for (2y+3)(2y-1)=5 equation:

Simplifying
(2y + 3)(2y + -1) = 5

Reorder the terms:
(3 + 2y)(2y + -1) = 5

Reorder the terms:
(3 + 2y)(-1 + 2y) = 5

Multiply (3 + 2y) * (-1 + 2y)
(3(-1 + 2y) + 2y * (-1 + 2y)) = 5
((-1 * 3 + 2y * 3) + 2y * (-1 + 2y)) = 5
((-3 + 6y) + 2y * (-1 + 2y)) = 5
(-3 + 6y + (-1 * 2y + 2y * 2y)) = 5
(-3 + 6y + (-2y + 4y2)) = 5

Combine like terms: 6y + -2y = 4y
(-3 + 4y + 4y2) = 5

Solving
-3 + 4y + 4y2 = 5

Solving for variable 'y'.

Reorder the terms:
-3 + -5 + 4y + 4y2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + 4y + 4y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + 4y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + y + y2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve:

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
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, 1}