105a^2-3a-18=0

Solution for 105a^2-3a-18=0 equation:

Simplifying
105a2 + -3a + -18 = 0

Reorder the terms:
-18 + -3a + 105a2 = 0

Solving
-18 + -3a + 105a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -1a + 35a2) = 0

Factor a trinomial.
3((-2 + -5a)(3 + -7a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -5a)' equal to zero and attempt to solve:

Simplifying
-2 + -5a = 0

Solving
-2 + -5a = 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 + -5a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5a = 0 + 2
-5a = 0 + 2

Combine like terms: 0 + 2 = 2
-5a = 2

Divide each side by '-5'.
a = -0.4

Simplifying
a = -0.4
Subproblem 2
Set the factor '(3 + -7a)' equal to zero and attempt to solve:

Simplifying
3 + -7a = 0

Solving
3 + -7a = 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 + -7a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7a = 0 + -3
-7a = 0 + -3

Combine like terms: 0 + -3 = -3
-7a = -3

Divide each side by '-7'.
a = 0.4285714286

Simplifying
a = 0.4285714286
Solution
a = {-0.4, 0.4285714286}