y(2y-1)(y+5)=0

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Solution for y(2y-1)(y+5)=0 equation:


Simplifying
y(2y + -1)(y + 5) = 0

Reorder the terms:
y(-1 + 2y)(y + 5) = 0

Reorder the terms:
y(-1 + 2y)(5 + y) = 0

Multiply (-1 + 2y) * (5 + y)
y(-1(5 + y) + 2y * (5 + y)) = 0
y((5 * -1 + y * -1) + 2y * (5 + y)) = 0
y((-5 + -1y) + 2y * (5 + y)) = 0
y(-5 + -1y + (5 * 2y + y * 2y)) = 0
y(-5 + -1y + (10y + 2y2)) = 0

Combine like terms: -1y + 10y = 9y
y(-5 + 9y + 2y2) = 0
(-5 * y + 9y * y + 2y2 * y) = 0
(-5y + 9y2 + 2y3) = 0

Solving
-5y + 9y2 + 2y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-5 + 9y + 2y2) = 0

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

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 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 + -1y = 0 + 5

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

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

Divide each side by '-1'.
y = -5

Simplifying
y = -5

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

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

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

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

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {0, -5, 0.5}

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