a^3+7a^2-8a=0

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Solution for a^3+7a^2-8a=0 equation:


Simplifying
a3 + 7a2 + -8a = 0

Reorder the terms:
-8a + 7a2 + a3 = 0

Solving
-8a + 7a2 + a3 = 0

Solving for variable 'a'.

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

Factor a trinomial.
a((-8 + -1a)(1 + -1a)) = 0

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 '(-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

Subproblem 3

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

Solution

a = {0, -8, 1}

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