-4(y-7)(-y-2)=0

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Solution for -4(y-7)(-y-2)=0 equation: 


Simplifying
-4(y + -7)(-1y + -2) = 0

Reorder the terms:
-4(-7 + y)(-1y + -2) = 0

Reorder the terms:
-4(-7 + y)(-2 + -1y) = 0

Multiply (-7 + y) * (-2 + -1y)
-4(-7(-2 + -1y) + y(-2 + -1y)) = 0
-4((-2 * -7 + -1y * -7) + y(-2 + -1y)) = 0
-4((14 + 7y) + y(-2 + -1y)) = 0
-4(14 + 7y + (-2 * y + -1y * y)) = 0
-4(14 + 7y + (-2y + -1y2)) = 0

Combine like terms: 7y + -2y = 5y
-4(14 + 5y + -1y2) = 0
(14 * -4 + 5y * -4 + -1y2 * -4) = 0
(-56 + -20y + 4y2) = 0

Solving
-56 + -20y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + -5y + y2) = 0

Factor a trinomial.
4((-2 + -1y)(7 + -1y)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2

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 = {-2, 7}

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