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

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


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

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

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

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

Combine like terms: 3y + -4y = -1y
(-12 + -1y + y2) = 8

Solving
-12 + -1y + y2 = 8

Solving for variable 'y'.

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

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

Combine like terms: 8 + -8 = 0
-20 + -1y + y2 = 0

Factor a trinomial.
(-4 + -1y)(5 + -1y) = 0


Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4

Subproblem 2
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
Solution
y = {-4, 5}

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