(2y+5)*(2y^2+25-10y)=8y^3+125

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Solution for (2y+5)*(2y^2+25-10y)=8y^3+125 equation:


Simplifying
(2y + 5)(2y2 + 25 + -10y) = 8y3 + 125

Reorder the terms:
(5 + 2y)(2y2 + 25 + -10y) = 8y3 + 125

Reorder the terms:
(5 + 2y)(25 + -10y + 2y2) = 8y3 + 125

Multiply (5 + 2y) * (25 + -10y + 2y2)
(5(25 + -10y + 2y2) + 2y * (25 + -10y + 2y2)) = 8y3 + 125
((25 * 5 + -10y * 5 + 2y2 * 5) + 2y * (25 + -10y + 2y2)) = 8y3 + 125
((125 + -50y + 10y2) + 2y * (25 + -10y + 2y2)) = 8y3 + 125
(125 + -50y + 10y2 + (25 * 2y + -10y * 2y + 2y2 * 2y)) = 8y3 + 125
(125 + -50y + 10y2 + (50y + -20y2 + 4y3)) = 8y3 + 125

Reorder the terms:
(125 + -50y + 50y + 10y2 + -20y2 + 4y3) = 8y3 + 125

Combine like terms: -50y + 50y = 0
(125 + 0 + 10y2 + -20y2 + 4y3) = 8y3 + 125
(125 + 10y2 + -20y2 + 4y3) = 8y3 + 125

Combine like terms: 10y2 + -20y2 = -10y2
(125 + -10y2 + 4y3) = 8y3 + 125

Reorder the terms:
125 + -10y2 + 4y3 = 125 + 8y3

Add '-125' to each side of the equation.
125 + -10y2 + -125 + 4y3 = 125 + -125 + 8y3

Reorder the terms:
125 + -125 + -10y2 + 4y3 = 125 + -125 + 8y3

Combine like terms: 125 + -125 = 0
0 + -10y2 + 4y3 = 125 + -125 + 8y3
-10y2 + 4y3 = 125 + -125 + 8y3

Combine like terms: 125 + -125 = 0
-10y2 + 4y3 = 0 + 8y3
-10y2 + 4y3 = 8y3

Solving
-10y2 + 4y3 = 8y3

Solving for variable 'y'.

Combine like terms: 4y3 + -8y3 = -4y3
-10y2 + -4y3 = 8y3 + -8y3

Combine like terms: 8y3 + -8y3 = 0
-10y2 + -4y3 = 0

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

Ignore the factor -2.

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 '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 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 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Divide each side by '2'. y = -2.5 Simplifying y = -2.5

Solution

y = {0, -2.5}

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