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

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


Simplifying
2x2 + (-1y + 8) = (2y + 3)(y + -4)

Reorder the terms:
2x2 + (8 + -1y) = (2y + 3)(y + -4)

Remove parenthesis around (8 + -1y)
2x2 + 8 + -1y = (2y + 3)(y + -4)

Reorder the terms:
8 + 2x2 + -1y = (2y + 3)(y + -4)

Reorder the terms:
8 + 2x2 + -1y = (3 + 2y)(y + -4)

Reorder the terms:
8 + 2x2 + -1y = (3 + 2y)(-4 + y)

Multiply (3 + 2y) * (-4 + y)
8 + 2x2 + -1y = (3(-4 + y) + 2y * (-4 + y))
8 + 2x2 + -1y = ((-4 * 3 + y * 3) + 2y * (-4 + y))
8 + 2x2 + -1y = ((-12 + 3y) + 2y * (-4 + y))
8 + 2x2 + -1y = (-12 + 3y + (-4 * 2y + y * 2y))
8 + 2x2 + -1y = (-12 + 3y + (-8y + 2y2))

Combine like terms: 3y + -8y = -5y
8 + 2x2 + -1y = (-12 + -5y + 2y2)

Solving
8 + 2x2 + -1y = -12 + -5y + 2y2

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + 2x2 + -8 + -1y = -12 + -5y + -8 + 2y2

Reorder the terms:
8 + -8 + 2x2 + -1y = -12 + -5y + -8 + 2y2

Combine like terms: 8 + -8 = 0
0 + 2x2 + -1y = -12 + -5y + -8 + 2y2
2x2 + -1y = -12 + -5y + -8 + 2y2

Reorder the terms:
2x2 + -1y = -12 + -8 + -5y + 2y2

Combine like terms: -12 + -8 = -20
2x2 + -1y = -20 + -5y + 2y2

Add 'y' to each side of the equation.
2x2 + -1y + y = -20 + -5y + y + 2y2

Combine like terms: -1y + y = 0
2x2 + 0 = -20 + -5y + y + 2y2
2x2 = -20 + -5y + y + 2y2

Combine like terms: -5y + y = -4y
2x2 = -20 + -4y + 2y2

Divide each side by '2'.
x2 = -10 + -2y + y2

Simplifying
x2 = -10 + -2y + y2

Reorder the terms:
10 + x2 + 2y + -1y2 = -10 + -2y + y2 + 10 + 2y + -1y2

Reorder the terms:
10 + x2 + 2y + -1y2 = -10 + 10 + -2y + 2y + y2 + -1y2

Combine like terms: -10 + 10 = 0
10 + x2 + 2y + -1y2 = 0 + -2y + 2y + y2 + -1y2
10 + x2 + 2y + -1y2 = -2y + 2y + y2 + -1y2

Combine like terms: -2y + 2y = 0
10 + x2 + 2y + -1y2 = 0 + y2 + -1y2
10 + x2 + 2y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
10 + x2 + 2y + -1y2 = 0

The solution to this equation could not be determined.

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