6a^2+18a=168

Solution for 6a^2+18a=168 equation:

Simplifying
6a2 + 18a = 168

Reorder the terms:
18a + 6a2 = 168

Solving
18a + 6a2 = 168

Solving for variable 'a'.

Reorder the terms:
-168 + 18a + 6a2 = 168 + -168

Combine like terms: 168 + -168 = 0
-168 + 18a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-28 + 3a + a2) = 0

Factor a trinomial.
6((-7 + -1a)(4 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve:

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 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 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-7, 4}