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

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

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

Reorder the terms:
5y(-3 + 2y) + (2y + -3) = (5y + 1)(2y + 3)
(-3 * 5y + 2y * 5y) + (2y + -3) = (5y + 1)(2y + 3)
(-15y + 10y2) + (2y + -3) = (5y + 1)(2y + 3)

Reorder the terms:
-15y + 10y2 + (-3 + 2y) = (5y + 1)(2y + 3)

Remove parenthesis around (-3 + 2y)
-15y + 10y2 + -3 + 2y = (5y + 1)(2y + 3)

Reorder the terms:
-3 + -15y + 2y + 10y2 = (5y + 1)(2y + 3)

Combine like terms: -15y + 2y = -13y
-3 + -13y + 10y2 = (5y + 1)(2y + 3)

Reorder the terms:
-3 + -13y + 10y2 = (1 + 5y)(2y + 3)

Reorder the terms:
-3 + -13y + 10y2 = (1 + 5y)(3 + 2y)

Multiply (1 + 5y) * (3 + 2y)
-3 + -13y + 10y2 = (1(3 + 2y) + 5y * (3 + 2y))
-3 + -13y + 10y2 = ((3 * 1 + 2y * 1) + 5y * (3 + 2y))
-3 + -13y + 10y2 = ((3 + 2y) + 5y * (3 + 2y))
-3 + -13y + 10y2 = (3 + 2y + (3 * 5y + 2y * 5y))
-3 + -13y + 10y2 = (3 + 2y + (15y + 10y2))

Combine like terms: 2y + 15y = 17y
-3 + -13y + 10y2 = (3 + 17y + 10y2)

Add '-10y2' to each side of the equation.
-3 + -13y + 10y2 + -10y2 = 3 + 17y + 10y2 + -10y2

Combine like terms: 10y2 + -10y2 = 0
-3 + -13y + 0 = 3 + 17y + 10y2 + -10y2
-3 + -13y = 3 + 17y + 10y2 + -10y2

Combine like terms: 10y2 + -10y2 = 0
-3 + -13y = 3 + 17y + 0
-3 + -13y = 3 + 17y

Solving
-3 + -13y = 3 + 17y

Solving for variable 'y'.

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

Add '-17y' to each side of the equation.
-3 + -13y + -17y = 3 + 17y + -17y

Combine like terms: -13y + -17y = -30y
-3 + -30y = 3 + 17y + -17y

Combine like terms: 17y + -17y = 0
-3 + -30y = 3 + 0
-3 + -30y = 3

Add '3' to each side of the equation.
-3 + 3 + -30y = 3 + 3

Combine like terms: -3 + 3 = 0
0 + -30y = 3 + 3
-30y = 3 + 3

Combine like terms: 3 + 3 = 6
-30y = 6

Divide each side by '-30'.
y = -0.2

Simplifying
y = -0.2