3a(a^2+5a)=-18a

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Solution for 3a(a^2+5a)=-18a equation:


Simplifying
3a(a2 + 5a) = -18a

Reorder the terms:
3a(5a + a2) = -18a
(5a * 3a + a2 * 3a) = -18a
(15a2 + 3a3) = -18a

Solving
15a2 + 3a3 = -18a

Solving for variable 'a'.

Reorder the terms:
18a + 15a2 + 3a3 = -18a + 18a

Combine like terms: -18a + 18a = 0
18a + 15a2 + 3a3 = 0

Factor out the Greatest Common Factor (GCF), '3a'.
3a(6 + 5a + a2) = 0

Factor a trinomial.
3a((3 + a)(2 + a)) = 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 '(3 + a)' equal to zero and attempt to solve: Simplifying 3 + a = 0 Solving 3 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + a = 0 + -3 a = 0 + -3 Combine like terms: 0 + -3 = -3 a = -3 Simplifying a = -3

Subproblem 3

Set the factor '(2 + a)' equal to zero and attempt to solve: Simplifying 2 + a = 0 Solving 2 + a = 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 + a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + a = 0 + -2 a = 0 + -2 Combine like terms: 0 + -2 = -2 a = -2 Simplifying a = -2

Solution

a = {0, -3, -2}

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