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

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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 = -13y
-3 + -13y + 10y2 = (-3 + -13y + 10y2)

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

Reorder the terms:
-3 + 3 + -13y + 10y2 = -3 + -13y + 3 + 10y2

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

Reorder the terms:
-13y + 10y2 = -3 + 3 + -13y + 10y2

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

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

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

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

Add '-10y2' to each side of the equation.
10y2 + -10y2 = 10y2 + -10y2

Combine like terms: 10y2 + -10y2 = 0
0 = 10y2 + -10y2

Combine like terms: 10y2 + -10y2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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