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

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


Simplifying
(y + -7) * 7(y + 9) = 0

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

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

Reorder the terms for easier multiplication:
7(-7 + y)(9 + y) = 0

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

Combine like terms: -7y + 9y = 2y
7(-63 + 2y + y2) = 0
(-63 * 7 + 2y * 7 + y2 * 7) = 0
(-441 + 14y + 7y2) = 0

Solving
-441 + 14y + 7y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-63 + 2y + y2) = 0

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

Ignore the factor 7.

Subproblem 1
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

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 = {-9, 7}

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