2y^2+(-y+8)=(2y+3)(y-4)

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Solution for 2y^2+(-y+8)=(2y+3)(y-4) equation: 


Simplifying
2y2 + (-1y + 8) = (2y + 3)(y + -4)

Reorder the terms:
2y2 + (8 + -1y) = (2y + 3)(y + -4)

Remove parenthesis around (8 + -1y)
2y2 + 8 + -1y = (2y + 3)(y + -4)

Reorder the terms:
8 + -1y + 2y2 = (2y + 3)(y + -4)

Reorder the terms:
8 + -1y + 2y2 = (3 + 2y)(y + -4)

Reorder the terms:
8 + -1y + 2y2 = (3 + 2y)(-4 + y)

Multiply (3 + 2y) * (-4 + y)
8 + -1y + 2y2 = (3(-4 + y) + 2y * (-4 + y))
8 + -1y + 2y2 = ((-4 * 3 + y * 3) + 2y * (-4 + y))
8 + -1y + 2y2 = ((-12 + 3y) + 2y * (-4 + y))
8 + -1y + 2y2 = (-12 + 3y + (-4 * 2y + y * 2y))
8 + -1y + 2y2 = (-12 + 3y + (-8y + 2y2))

Combine like terms: 3y + -8y = -5y
8 + -1y + 2y2 = (-12 + -5y + 2y2)

Add '-2y2' to each side of the equation.
8 + -1y + 2y2 + -2y2 = -12 + -5y + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
8 + -1y + 0 = -12 + -5y + 2y2 + -2y2
8 + -1y = -12 + -5y + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
8 + -1y = -12 + -5y + 0
8 + -1y = -12 + -5y

Solving
8 + -1y = -12 + -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.
8 + -1y + 5y = -12 + -5y + 5y

Combine like terms: -1y + 5y = 4y
8 + 4y = -12 + -5y + 5y

Combine like terms: -5y + 5y = 0
8 + 4y = -12 + 0
8 + 4y = -12

Add '-8' to each side of the equation.
8 + -8 + 4y = -12 + -8

Combine like terms: 8 + -8 = 0
0 + 4y = -12 + -8
4y = -12 + -8

Combine like terms: -12 + -8 = -20
4y = -20

Divide each side by '4'.
y = -5

Simplifying
y = -5

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