27a^3+18a^2=-3a

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Solution for 27a^3+18a^2=-3a equation:


Simplifying
27a3 + 18a2 = -3a

Reorder the terms:
18a2 + 27a3 = -3a

Solving
18a2 + 27a3 = -3a

Solving for variable 'a'.

Reorder the terms:
3a + 18a2 + 27a3 = -3a + 3a

Combine like terms: -3a + 3a = 0
3a + 18a2 + 27a3 = 0

Factor out the Greatest Common Factor (GCF), '3a'.
3a(1 + 6a + 9a2) = 0

Factor a trinomial.
3a((1 + 3a)(1 + 3a)) = 0

Ignore the factor 3.

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 + 3a)' equal to zero and attempt to solve: Simplifying 1 + 3a = 0 Solving 1 + 3a = 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 + 3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3a = 0 + -1 3a = 0 + -1 Combine like terms: 0 + -1 = -1 3a = -1 Divide each side by '3'. a = -0.3333333333 Simplifying a = -0.3333333333

Subproblem 3

Set the factor '(1 + 3a)' equal to zero and attempt to solve: Simplifying 1 + 3a = 0 Solving 1 + 3a = 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 + 3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3a = 0 + -1 3a = 0 + -1 Combine like terms: 0 + -1 = -1 3a = -1 Divide each side by '3'. a = -0.3333333333 Simplifying a = -0.3333333333

Solution

a = {0, -0.3333333333, -0.3333333333}

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