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

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


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

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

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

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

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

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

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

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

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

Combine like terms: -15y + 2y = -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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