y^2(5y+10)(5y-10)=

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Solution for y^2(5y+10)(5y-10)= equation: 


Simplifying
y2(5y + 10)(5y + -10) = 0

Reorder the terms:
y2(10 + 5y)(5y + -10) = 0

Reorder the terms:
y2(10 + 5y)(-10 + 5y) = 0

Multiply (10 + 5y) * (-10 + 5y)
y2(10(-10 + 5y) + 5y * (-10 + 5y)) = 0
y2((-10 * 10 + 5y * 10) + 5y * (-10 + 5y)) = 0
y2((-100 + 50y) + 5y * (-10 + 5y)) = 0
y2(-100 + 50y + (-10 * 5y + 5y * 5y)) = 0
y2(-100 + 50y + (-50y + 25y2)) = 0

Combine like terms: 50y + -50y = 0
y2(-100 + 0 + 25y2) = 0
y2(-100 + 25y2) = 0
(-100 * y2 + 25y2 * y2) = 0
(-100y2 + 25y4) = 0

Solving
-100y2 + 25y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '25y2'.
25y2(-4 + y2) = 0

Factor a difference between two squares.
25y2((2 + y)(-2 + y)) = 0

Ignore the factor 25.

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}

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

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2

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

Simplifying
-2 + y = 0

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

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

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

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

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