(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.
(-5 + -1y)(4 + -1y) = 0


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 '(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
Solution
y = {-5, 4}

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