-30a^2+51a-18=0

Solution for -30a^2+51a-18=0 equation:

Simplifying
-30a2 + 51a + -18 = 0

Reorder the terms:
-18 + 51a + -30a2 = 0

Solving
-18 + 51a + -30a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 17a + -10a2) = 0

Factor a trinomial.
3((-6 + 5a)(1 + -2a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + 5a)' equal to zero and attempt to solve:

Simplifying
-6 + 5a = 0

Solving
-6 + 5a = 0

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

Add '6' to each side of the equation.
-6 + 6 + 5a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 5a = 0 + 6
5a = 0 + 6

Combine like terms: 0 + 6 = 6
5a = 6

Divide each side by '5'.
a = 1.2

Simplifying
a = 1.2
Subproblem 2
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 = {1.2, 0.5}