4y(y+3)(y-7)=0

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Solution for 4y(y+3)(y-7)=0 equation: 


Simplifying
4y(y + 3)(y + -7) = 0

Reorder the terms:
4y(3 + y)(y + -7) = 0

Reorder the terms:
4y(3 + y)(-7 + y) = 0

Multiply (3 + y) * (-7 + y)
4y(3(-7 + y) + y(-7 + y)) = 0
4y((-7 * 3 + y * 3) + y(-7 + y)) = 0
4y((-21 + 3y) + y(-7 + y)) = 0
4y(-21 + 3y + (-7 * y + y * y)) = 0
4y(-21 + 3y + (-7y + y2)) = 0

Combine like terms: 3y + -7y = -4y
4y(-21 + -4y + y2) = 0
(-21 * 4y + -4y * 4y + y2 * 4y) = 0
(-84y + -16y2 + 4y3) = 0

Solving
-84y + -16y2 + 4y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(-21 + -4y + y2) = 0

Factor a trinomial.
4y((-3 + -1y)(7 + -1y)) = 0

Ignore the factor 4.

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 '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 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 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3

Subproblem 3
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 = {0, -3, 7}

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