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

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

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

Reorder the terms:
5y(-3 + 2y) = (2y + -3)
(-3 * 5y + 2y * 5y) = (2y + -3)
(-15y + 10y2) = (2y + -3)

Reorder the terms:
-15y + 10y2 = (-3 + 2y)

Remove parenthesis around (-3 + 2y)
-15y + 10y2 = -3 + 2y

Solving
-15y + 10y2 = -3 + 2y

Solving for variable 'y'.

Reorder the terms:
3 + -15y + -2y + 10y2 = -3 + 2y + 3 + -2y

Combine like terms: -15y + -2y = -17y
3 + -17y + 10y2 = -3 + 2y + 3 + -2y

Reorder the terms:
3 + -17y + 10y2 = -3 + 3 + 2y + -2y

Combine like terms: -3 + 3 = 0
3 + -17y + 10y2 = 0 + 2y + -2y
3 + -17y + 10y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
3 + -17y + 10y2 = 0

Factor a trinomial.
(1 + -5y)(3 + -2y) = 0

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

Simplifying
1 + -5y = 0

Solving
1 + -5y = 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 + -5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5y = 0 + -1
-5y = 0 + -1

Combine like terms: 0 + -1 = -1
-5y = -1

Divide each side by '-5'.
y = 0.2

Simplifying
y = 0.2
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 = {0.2, 1.5}