18a^3+51a^2-42a=

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Solution for 18a^3+51a^2-42a= equation:


Simplifying
18a3 + 51a2 + -42a = 0

Reorder the terms:
-42a + 51a2 + 18a3 = 0

Solving
-42a + 51a2 + 18a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-14 + 17a + 6a2) = 0

Factor a trinomial.
3a((-7 + -2a)(2 + -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 '(-7 + -2a)' equal to zero and attempt to solve: Simplifying -7 + -2a = 0 Solving -7 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2a = 0 + 7 -2a = 0 + 7 Combine like terms: 0 + 7 = 7 -2a = 7 Divide each side by '-2'. a = -3.5 Simplifying a = -3.5

Subproblem 3

Set the factor '(2 + -3a)' equal to zero and attempt to solve: Simplifying 2 + -3a = 0 Solving 2 + -3a = 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 + -3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3a = 0 + -2 -3a = 0 + -2 Combine like terms: 0 + -2 = -2 -3a = -2 Divide each side by '-3'. a = 0.6666666667 Simplifying a = 0.6666666667

Solution

a = {0, -3.5, 0.6666666667}

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