8a^3-40a=4a^2

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Solution for 8a^3-40a=4a^2 equation:


Simplifying
8a3 + -40a = 4a2

Reorder the terms:
-40a + 8a3 = 4a2

Solving
-40a + 8a3 = 4a2

Solving for variable 'a'.

Reorder the terms:
-40a + -4a2 + 8a3 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
-40a + -4a2 + 8a3 = 0

Factor out the Greatest Common Factor (GCF), '4a'.
4a(-10 + -1a + 2a2) = 0

Factor a trinomial.
4a((-2 + -1a)(5 + -2a)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0

Subproblem 2

Set the factor '(-2 + -1a)' equal to zero and attempt to solve: Simplifying -2 + -1a = 0 Solving -2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a = 0 + 2 -1a = 0 + 2 Combine like terms: 0 + 2 = 2 -1a = 2 Divide each side by '-1'. a = -2 Simplifying a = -2

Subproblem 3

Set the factor '(5 + -2a)' equal to zero and attempt to solve: Simplifying 5 + -2a = 0 Solving 5 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2a = 0 + -5 -2a = 0 + -5 Combine like terms: 0 + -5 = -5 -2a = -5 Divide each side by '-2'. a = 2.5 Simplifying a = 2.5

Solution

a = {0, -2, 2.5}

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