4y(3y+5)(y-7)=0

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Solution for 4y(3y+5)(y-7)=0 equation: 


Simplifying
4y(3y + 5)(y + -7) = 0

Reorder the terms:
4y(5 + 3y)(y + -7) = 0

Reorder the terms:
4y(5 + 3y)(-7 + y) = 0

Multiply (5 + 3y) * (-7 + y)
4y(5(-7 + y) + 3y * (-7 + y)) = 0
4y((-7 * 5 + y * 5) + 3y * (-7 + y)) = 0
4y((-35 + 5y) + 3y * (-7 + y)) = 0
4y(-35 + 5y + (-7 * 3y + y * 3y)) = 0
4y(-35 + 5y + (-21y + 3y2)) = 0

Combine like terms: 5y + -21y = -16y
4y(-35 + -16y + 3y2) = 0
(-35 * 4y + -16y * 4y + 3y2 * 4y) = 0
(-140y + -64y2 + 12y3) = 0

Solving
-140y + -64y2 + 12y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(-35 + -16y + 3y2) = 0

Factor a trinomial.
4y((-5 + -3y)(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 '(-5 + -3y)' equal to zero and attempt to solve:

Simplifying
-5 + -3y = 0

Solving
-5 + -3y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3y = 0 + 5
-3y = 0 + 5

Combine like terms: 0 + 5 = 5
-3y = 5

Divide each side by '-3'.
y = -1.666666667

Simplifying
y = -1.666666667

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, -1.666666667, 7}

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