(y+6)(y+4)=8

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Solution for (y+6)(y+4)=8 equation:


Simplifying
(y + 6)(y + 4) = 8

Reorder the terms:
(6 + y)(y + 4) = 8

Reorder the terms:
(6 + y)(4 + y) = 8

Multiply (6 + y) * (4 + y)
(6(4 + y) + y(4 + y)) = 8
((4 * 6 + y * 6) + y(4 + y)) = 8
((24 + 6y) + y(4 + y)) = 8
(24 + 6y + (4 * y + y * y)) = 8
(24 + 6y + (4y + y2)) = 8

Combine like terms: 6y + 4y = 10y
(24 + 10y + y2) = 8

Solving
24 + 10y + y2 = 8

Solving for variable 'y'.

Reorder the terms:
24 + -8 + 10y + y2 = 8 + -8

Combine like terms: 24 + -8 = 16
16 + 10y + y2 = 8 + -8

Combine like terms: 8 + -8 = 0
16 + 10y + y2 = 0

Factor a trinomial.
(8 + y)(2 + y) = 0


Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

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

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

Simplifying
y = -8

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 = {-8, -2}

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