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

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

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

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

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

Multiply (-3 + y) * (3 + 2y)
(-3(3 + 2y) + y(3 + 2y)) = 5
((3 * -3 + 2y * -3) + y(3 + 2y)) = 5
((-9 + -6y) + y(3 + 2y)) = 5
(-9 + -6y + (3 * y + 2y * y)) = 5
(-9 + -6y + (3y + 2y2)) = 5

Combine like terms: -6y + 3y = -3y
(-9 + -3y + 2y2) = 5

Solving
-9 + -3y + 2y2 = 5

Solving for variable 'y'.

Reorder the terms:
-9 + -5 + -3y + 2y2 = 5 + -5

Combine like terms: -9 + -5 = -14
-14 + -3y + 2y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-14 + -3y + 2y2 = 0

Factor a trinomial.
(-2 + -1y)(7 + -2y) = 0

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 '(7 + -2y)' equal to zero and attempt to solve:

Simplifying
7 + -2y = 0

Solving
7 + -2y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {-2, 3.5}