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

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


Simplifying
2y(5y2 + -2)(5y2 + -2) = 0

Reorder the terms:
2y(-2 + 5y2)(5y2 + -2) = 0

Reorder the terms:
2y(-2 + 5y2)(-2 + 5y2) = 0

Multiply (-2 + 5y2) * (-2 + 5y2)
2y(-2(-2 + 5y2) + 5y2 * (-2 + 5y2)) = 0
2y((-2 * -2 + 5y2 * -2) + 5y2 * (-2 + 5y2)) = 0
2y((4 + -10y2) + 5y2 * (-2 + 5y2)) = 0
2y(4 + -10y2 + (-2 * 5y2 + 5y2 * 5y2)) = 0
2y(4 + -10y2 + (-10y2 + 25y4)) = 0

Combine like terms: -10y2 + -10y2 = -20y2
2y(4 + -20y2 + 25y4) = 0
(4 * 2y + -20y2 * 2y + 25y4 * 2y) = 0
(8y + -40y3 + 50y5) = 0

Solving
8y + -40y3 + 50y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(4 + -20y2 + 25y4) = 0

Factor a trinomial.
2y((2 + -5y2)(2 + -5y2)) = 0

Ignore the factor 2.

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 + -5y2)' equal to zero and attempt to solve:

Simplifying
2 + -5y2 = 0

Solving
2 + -5y2 = 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 + -5y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y2 = 0 + -2
-5y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5y2 = -2

Divide each side by '-5'.
y2 = 0.4

Simplifying
y2 = 0.4

Take the square root of each side:
y = {-0.632455532, 0.632455532}

Subproblem 3
Set the factor '(2 + -5y2)' equal to zero and attempt to solve:

Simplifying
2 + -5y2 = 0

Solving
2 + -5y2 = 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 + -5y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y2 = 0 + -2
-5y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5y2 = -2

Divide each side by '-5'.
y2 = 0.4

Simplifying
y2 = 0.4

Take the square root of each side:
y = {-0.632455532, 0.632455532}
Solution
y = {0, -0.632455532, 0.632455532, -0.632455532, 0.632455532}

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