y(y+3)(y+7)=0

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Solution for y(y+3)(y+7)=0 equation: 


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

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

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

Multiply (3 + y) * (7 + y)
y(3(7 + y) + y(7 + y)) = 0
y((7 * 3 + y * 3) + y(7 + y)) = 0
y((21 + 3y) + y(7 + y)) = 0
y(21 + 3y + (7 * y + y * y)) = 0
y(21 + 3y + (7y + y2)) = 0

Combine like terms: 3y + 7y = 10y
y(21 + 10y + y2) = 0
(21 * y + 10y * y + y2 * y) = 0
(21y + 10y2 + y3) = 0

Solving
21y + 10y2 + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(21 + 10y + y2) = 0

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


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

Simplifying
7 + y = 0

Solving
7 + y = 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 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7

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

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {0, -7, -3}

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