y(y+2)(7y-1)=0

Solution for y(y+2)(7y-1)=0 equation:

Simplifying
y(y + 2)(7y + -1) = 0

Reorder the terms:
y(2 + y)(7y + -1) = 0

Reorder the terms:
y(2 + y)(-1 + 7y) = 0

Multiply (2 + y) * (-1 + 7y)
y(2(-1 + 7y) + y(-1 + 7y)) = 0
y((-1 * 2 + 7y * 2) + y(-1 + 7y)) = 0
y((-2 + 14y) + y(-1 + 7y)) = 0
y(-2 + 14y + (-1 * y + 7y * y)) = 0
y(-2 + 14y + (-1y + 7y2)) = 0

Combine like terms: 14y + -1y = 13y
y(-2 + 13y + 7y2) = 0
(-2 * y + 13y * y + 7y2 * y) = 0
(-2y + 13y2 + 7y3) = 0

Solving
-2y + 13y2 + 7y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-2 + 13y + 7y2) = 0

Factor a trinomial.
y((-2 + -1y)(1 + -7y)) = 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 '(-2 + -1y)' equal to zero and attempt to solve:

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
Subproblem 3
Set the factor '(1 + -7y)' equal to zero and attempt to solve:

Simplifying
1 + -7y = 0

Solving
1 + -7y = 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 + -7y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7y = 0 + -1
-7y = 0 + -1

Combine like terms: 0 + -1 = -1
-7y = -1

Divide each side by '-7'.
y = 0.1428571429

Simplifying
y = 0.1428571429
Solution
y = {0, -2, 0.1428571429}