(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 = -12y
(-63 + -12y + 3y2) = 0

Solving
-63 + -12y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + -4y + y2) = 0

Factor a trinomial.
3((-3 + -1y)(7 + -1y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 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 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3

Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

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

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