4a^3-28a^2=32a

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Solution for 4a^3-28a^2=32a equation:


Simplifying
4a3 + -28a2 = 32a

Reorder the terms:
-28a2 + 4a3 = 32a

Solving
-28a2 + 4a3 = 32a

Solving for variable 'a'.

Reorder the terms:
-32a + -28a2 + 4a3 = 32a + -32a

Combine like terms: 32a + -32a = 0
-32a + -28a2 + 4a3 = 0

Factor out the Greatest Common Factor (GCF), '4a'.
4a(-8 + -7a + a2) = 0

Factor a trinomial.
4a((-1 + -1a)(8 + -1a)) = 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 '(-1 + -1a)' equal to zero and attempt to solve: Simplifying -1 + -1a = 0 Solving -1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1a = 0 + 1 -1a = 0 + 1 Combine like terms: 0 + 1 = 1 -1a = 1 Divide each side by '-1'. a = -1 Simplifying a = -1

Subproblem 3

Set the factor '(8 + -1a)' equal to zero and attempt to solve: Simplifying 8 + -1a = 0 Solving 8 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1a = 0 + -8 -1a = 0 + -8 Combine like terms: 0 + -8 = -8 -1a = -8 Divide each side by '-1'. a = 8 Simplifying a = 8

Solution

a = {0, -1, 8}

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