-3(y-1)(-y-7)=0

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Solution for -3(y-1)(-y-7)=0 equation: 


Simplifying
-3(y + -1)(-1y + -7) = 0

Reorder the terms:
-3(-1 + y)(-1y + -7) = 0

Reorder the terms:
-3(-1 + y)(-7 + -1y) = 0

Multiply (-1 + y) * (-7 + -1y)
-3(-1(-7 + -1y) + y(-7 + -1y)) = 0
-3((-7 * -1 + -1y * -1) + y(-7 + -1y)) = 0
-3((7 + 1y) + y(-7 + -1y)) = 0
-3(7 + 1y + (-7 * y + -1y * y)) = 0
-3(7 + 1y + (-7y + -1y2)) = 0

Combine like terms: 1y + -7y = -6y
-3(7 + -6y + -1y2) = 0
(7 * -3 + -6y * -3 + -1y2 * -3) = 0
(-21 + 18y + 3y2) = 0

Solving
-21 + 18y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 6y + y2) = 0

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

Ignore the factor 3.

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 '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-7, 1}

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