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

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


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

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

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

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

Combine like terms: 2y + -1y = 1y
8 + 1y = (2y + 3)(y + -4)

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

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

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

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

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

Solving for variable 'y'.

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

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

Combine like terms: 1y + 5y = 6y
20 + 6y + -2y2 = -12 + -5y + 2y2 + 12 + 5y + -2y2

Reorder the terms:
20 + 6y + -2y2 = -12 + 12 + -5y + 5y + 2y2 + -2y2

Combine like terms: -12 + 12 = 0
20 + 6y + -2y2 = 0 + -5y + 5y + 2y2 + -2y2
20 + 6y + -2y2 = -5y + 5y + 2y2 + -2y2

Combine like terms: -5y + 5y = 0
20 + 6y + -2y2 = 0 + 2y2 + -2y2
20 + 6y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
20 + 6y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 3y + -1y2) = 0

Factor a trinomial.
2((5 + -1y)(2 + y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5

Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Solution
y = {5, -2}

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