(4-3y)*(2y+3)=5y

Solution for (4-3y)*(2y+3)=5y equation:

Simplifying
(4 + -3y)(2y + 3) = 5y

Reorder the terms:
(4 + -3y)(3 + 2y) = 5y

Multiply (4 + -3y) * (3 + 2y)
(4(3 + 2y) + -3y * (3 + 2y)) = 5y
((3 * 4 + 2y * 4) + -3y * (3 + 2y)) = 5y
((12 + 8y) + -3y * (3 + 2y)) = 5y
(12 + 8y + (3 * -3y + 2y * -3y)) = 5y
(12 + 8y + (-9y + -6y2)) = 5y

Combine like terms: 8y + -9y = -1y
(12 + -1y + -6y2) = 5y

Solving
12 + -1y + -6y2 = 5y

Solving for variable 'y'.

Reorder the terms:
12 + -1y + -5y + -6y2 = 5y + -5y

Combine like terms: -1y + -5y = -6y
12 + -6y + -6y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
12 + -6y + -6y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + -1y + -1y2) = 0

Factor a trinomial.
6((1 + -1y)(2 + y)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2
Solution
y = {1, -2}