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

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Solution for 4(y-7)(-y-1)=0 equation: 


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

Reorder the terms:
4(-7 + y)(-1y + -1) = 0

Reorder the terms:
4(-7 + y)(-1 + -1y) = 0

Multiply (-7 + y) * (-1 + -1y)
4(-7(-1 + -1y) + y(-1 + -1y)) = 0
4((-1 * -7 + -1y * -7) + y(-1 + -1y)) = 0
4((7 + 7y) + y(-1 + -1y)) = 0
4(7 + 7y + (-1 * y + -1y * y)) = 0
4(7 + 7y + (-1y + -1y2)) = 0

Combine like terms: 7y + -1y = 6y
4(7 + 6y + -1y2) = 0
(7 * 4 + 6y * 4 + -1y2 * 4) = 0
(28 + 24y + -4y2) = 0

Solving
28 + 24y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + 6y + -1y2) = 0

Factor a trinomial.
4((7 + -1y)(1 + y)) = 0

Ignore the factor 4.

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 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

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

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

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

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

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