-5(y-9)(-y-7)=0

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Solution for -5(y-9)(-y-7)=0 equation: 


Simplifying
-5(y + -9)(-1y + -7) = 0

Reorder the terms:
-5(-9 + y)(-1y + -7) = 0

Reorder the terms:
-5(-9 + y)(-7 + -1y) = 0

Multiply (-9 + y) * (-7 + -1y)
-5(-9(-7 + -1y) + y(-7 + -1y)) = 0
-5((-7 * -9 + -1y * -9) + y(-7 + -1y)) = 0
-5((63 + 9y) + y(-7 + -1y)) = 0
-5(63 + 9y + (-7 * y + -1y * y)) = 0
-5(63 + 9y + (-7y + -1y2)) = 0

Combine like terms: 9y + -7y = 2y
-5(63 + 2y + -1y2) = 0
(63 * -5 + 2y * -5 + -1y2 * -5) = 0
(-315 + -10y + 5y2) = 0

Solving
-315 + -10y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-63 + -2y + y2) = 0

Factor a trinomial.
5((-7 + -1y)(9 + -1y)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
Set the factor '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {-7, 9}

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