(3y+9)(y+7)=0

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Solution for (3y+9)(y+7)=0 equation: 


Simplifying
(3y + 9)(y + 7) = 0

Reorder the terms:
(9 + 3y)(y + 7) = 0

Reorder the terms:
(9 + 3y)(7 + y) = 0

Multiply (9 + 3y) * (7 + y)
(9(7 + y) + 3y * (7 + y)) = 0
((7 * 9 + y * 9) + 3y * (7 + y)) = 0
((63 + 9y) + 3y * (7 + y)) = 0
(63 + 9y + (7 * 3y + y * 3y)) = 0
(63 + 9y + (21y + 3y2)) = 0

Combine like terms: 9y + 21y = 30y
(63 + 30y + 3y2) = 0

Solving
63 + 30y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + 10y + y2) = 0

Factor a trinomial.
3((7 + y)(3 + y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7

Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {-7, -3}

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