5y(5y+1)(8y+7)=0

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Solution for 5y(5y+1)(8y+7)=0 equation: 


Simplifying
5y(5y + 1)(8y + 7) = 0

Reorder the terms:
5y(1 + 5y)(8y + 7) = 0

Reorder the terms:
5y(1 + 5y)(7 + 8y) = 0

Multiply (1 + 5y) * (7 + 8y)
5y(1(7 + 8y) + 5y * (7 + 8y)) = 0
5y((7 * 1 + 8y * 1) + 5y * (7 + 8y)) = 0
5y((7 + 8y) + 5y * (7 + 8y)) = 0
5y(7 + 8y + (7 * 5y + 8y * 5y)) = 0
5y(7 + 8y + (35y + 40y2)) = 0

Combine like terms: 8y + 35y = 43y
5y(7 + 43y + 40y2) = 0
(7 * 5y + 43y * 5y + 40y2 * 5y) = 0
(35y + 215y2 + 200y3) = 0

Solving
35y + 215y2 + 200y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(7 + 43y + 40y2) = 0

Factor a trinomial.
5y((7 + 8y)(1 + 5y)) = 0

Ignore the factor 5.

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 + 8y)' equal to zero and attempt to solve:

Simplifying
7 + 8y = 0

Solving
7 + 8y = 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 + 8y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 8y = 0 + -7
8y = 0 + -7

Combine like terms: 0 + -7 = -7
8y = -7

Divide each side by '8'.
y = -0.875

Simplifying
y = -0.875

Subproblem 3
Set the factor '(1 + 5y)' equal to zero and attempt to solve:

Simplifying
1 + 5y = 0

Solving
1 + 5y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5y = 0 + -1
5y = 0 + -1

Combine like terms: 0 + -1 = -1
5y = -1

Divide each side by '5'.
y = -0.2

Simplifying
y = -0.2
Solution
y = {0, -0.875, -0.2}

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