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

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


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

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

Combine like terms: 2y + -2y = 0
7y((-4 + 0 + y2)) = 0
7y((-4 + y2)) = 0
(-4 * 7y + y2 * 7y) = 0
(-28y + 7y3) = 0

Solving
-28y + 7y3 = 0

Solving for variable 'y'.

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

Factor a difference between two squares.
7y((2 + y)(-2 + y)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

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

Simplifying
2 + y = 0

Solving
2 + y = 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 + y = 0 + -2

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

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

Simplifying
y = -2

Subproblem 3
Set the factor '(-2 + y)' equal to zero and attempt to solve:

Simplifying
-2 + y = 0

Solving
-2 + y = 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 + y = 0 + 2

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

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

Simplifying
y = 2
Solution
y = {0, -2, 2}

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