2*3a^2-5(3a)+6=0

Solution for 2*3a^2-5(3a)+6=0 equation:

Simplifying
2 * 3a2 + -5(3a) + 6 = 0

Multiply 2 * 3
6a2 + -5(3a) + 6 = 0

Remove parenthesis around (3a)
6a2 + -5 * 3a + 6 = 0

Multiply -5 * 3
6a2 + -15a + 6 = 0

Reorder the terms:
6 + -15a + 6a2 = 0

Solving
6 + -15a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -5a + 2a2) = 0

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

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 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 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {0.5, 2}