2y(2y+6)=2y(y-4)

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Solution for 2y(2y+6)=2y(y-4) equation: 


Simplifying
2y(2y + 6) = 2y(y + -4)

Reorder the terms:
2y(6 + 2y) = 2y(y + -4)
(6 * 2y + 2y * 2y) = 2y(y + -4)
(12y + 4y2) = 2y(y + -4)

Reorder the terms:
12y + 4y2 = 2y(-4 + y)
12y + 4y2 = (-4 * 2y + y * 2y)
12y + 4y2 = (-8y + 2y2)

Solving
12y + 4y2 = -8y + 2y2

Solving for variable 'y'.

Reorder the terms:
12y + 8y + 4y2 + -2y2 = -8y + 2y2 + 8y + -2y2

Combine like terms: 12y + 8y = 20y
20y + 4y2 + -2y2 = -8y + 2y2 + 8y + -2y2

Combine like terms: 4y2 + -2y2 = 2y2
20y + 2y2 = -8y + 2y2 + 8y + -2y2

Reorder the terms:
20y + 2y2 = -8y + 8y + 2y2 + -2y2

Combine like terms: -8y + 8y = 0
20y + 2y2 = 0 + 2y2 + -2y2
20y + 2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
20y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2y'.
2y(10 + y) = 0

Ignore the factor 2.

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

Simplifying
10 + y = 0

Solving
10 + y = 0

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

Add '-10' to each side of the equation.
10 + -10 + y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + y = 0 + -10
y = 0 + -10

Combine like terms: 0 + -10 = -10
y = -10

Simplifying
y = -10
Solution
y = {0, -10}

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