y(5y+13)(y-2)=0

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Solution for y(5y+13)(y-2)=0 equation: 


Simplifying
y(5y + 13)(y + -2) = 0

Reorder the terms:
y(13 + 5y)(y + -2) = 0

Reorder the terms:
y(13 + 5y)(-2 + y) = 0

Multiply (13 + 5y) * (-2 + y)
y(13(-2 + y) + 5y * (-2 + y)) = 0
y((-2 * 13 + y * 13) + 5y * (-2 + y)) = 0
y((-26 + 13y) + 5y * (-2 + y)) = 0
y(-26 + 13y + (-2 * 5y + y * 5y)) = 0
y(-26 + 13y + (-10y + 5y2)) = 0

Combine like terms: 13y + -10y = 3y
y(-26 + 3y + 5y2) = 0
(-26 * y + 3y * y + 5y2 * y) = 0
(-26y + 3y2 + 5y3) = 0

Solving
-26y + 3y2 + 5y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-26 + 3y + 5y2) = 0

Factor a trinomial.
y((-13 + -5y)(2 + -1y)) = 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 '(-13 + -5y)' equal to zero and attempt to solve:

Simplifying
-13 + -5y = 0

Solving
-13 + -5y = 0

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

Add '13' to each side of the equation.
-13 + 13 + -5y = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -5y = 0 + 13
-5y = 0 + 13

Combine like terms: 0 + 13 = 13
-5y = 13

Divide each side by '-5'.
y = -2.6

Simplifying
y = -2.6

Subproblem 3
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
Solution
y = {0, -2.6, 2}

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