(y+1)(2y+5)=(2y+3)(y-4)+5

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Solution for (y+1)(2y+5)=(2y+3)(y-4)+5 equation: 


Simplifying
(y + 1)(2y + 5) = (2y + 3)(y + -4) + 5

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

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

Multiply (1 + y) * (5 + 2y)
(1(5 + 2y) + y(5 + 2y)) = (2y + 3)(y + -4) + 5
((5 * 1 + 2y * 1) + y(5 + 2y)) = (2y + 3)(y + -4) + 5
((5 + 2y) + y(5 + 2y)) = (2y + 3)(y + -4) + 5
(5 + 2y + (5 * y + 2y * y)) = (2y + 3)(y + -4) + 5
(5 + 2y + (5y + 2y2)) = (2y + 3)(y + -4) + 5

Combine like terms: 2y + 5y = 7y
(5 + 7y + 2y2) = (2y + 3)(y + -4) + 5

Reorder the terms:
5 + 7y + 2y2 = (3 + 2y)(y + -4) + 5

Reorder the terms:
5 + 7y + 2y2 = (3 + 2y)(-4 + y) + 5

Multiply (3 + 2y) * (-4 + y)
5 + 7y + 2y2 = (3(-4 + y) + 2y * (-4 + y)) + 5
5 + 7y + 2y2 = ((-4 * 3 + y * 3) + 2y * (-4 + y)) + 5
5 + 7y + 2y2 = ((-12 + 3y) + 2y * (-4 + y)) + 5
5 + 7y + 2y2 = (-12 + 3y + (-4 * 2y + y * 2y)) + 5
5 + 7y + 2y2 = (-12 + 3y + (-8y + 2y2)) + 5

Combine like terms: 3y + -8y = -5y
5 + 7y + 2y2 = (-12 + -5y + 2y2) + 5

Reorder the terms:
5 + 7y + 2y2 = -12 + 5 + -5y + 2y2

Combine like terms: -12 + 5 = -7
5 + 7y + 2y2 = -7 + -5y + 2y2

Add '-2y2' to each side of the equation.
5 + 7y + 2y2 + -2y2 = -7 + -5y + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
5 + 7y + 0 = -7 + -5y + 2y2 + -2y2
5 + 7y = -7 + -5y + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
5 + 7y = -7 + -5y + 0
5 + 7y = -7 + -5y

Solving
5 + 7y = -7 + -5y

Solving for variable 'y'.

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

Add '5y' to each side of the equation.
5 + 7y + 5y = -7 + -5y + 5y

Combine like terms: 7y + 5y = 12y
5 + 12y = -7 + -5y + 5y

Combine like terms: -5y + 5y = 0
5 + 12y = -7 + 0
5 + 12y = -7

Add '-5' to each side of the equation.
5 + -5 + 12y = -7 + -5

Combine like terms: 5 + -5 = 0
0 + 12y = -7 + -5
12y = -7 + -5

Combine like terms: -7 + -5 = -12
12y = -12

Divide each side by '12'.
y = -1

Simplifying
y = -1

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