6a^3+13a^2+5a=0

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Solution for 6a^3+13a^2+5a=0 equation:


Simplifying
6a3 + 13a2 + 5a = 0

Reorder the terms:
5a + 13a2 + 6a3 = 0

Solving
5a + 13a2 + 6a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(5 + 13a + 6a2) = 0

Factor a trinomial.
a((5 + 3a)(1 + 2a)) = 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 '(5 + 3a)' equal to zero and attempt to solve: Simplifying 5 + 3a = 0 Solving 5 + 3a = 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 + 3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3a = 0 + -5 3a = 0 + -5 Combine like terms: 0 + -5 = -5 3a = -5 Divide each side by '3'. a = -1.666666667 Simplifying a = -1.666666667

Subproblem 3

Set the factor '(1 + 2a)' equal to zero and attempt to solve: Simplifying 1 + 2a = 0 Solving 1 + 2a = 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 + 2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2a = 0 + -1 2a = 0 + -1 Combine like terms: 0 + -1 = -1 2a = -1 Divide each side by '2'. a = -0.5 Simplifying a = -0.5

Solution

a = {0, -1.666666667, -0.5}

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