6a^2-13a+15=6a

Solution for 6a^2-13a+15=6a equation:

Simplifying
6a2 + -13a + 15 = 6a

Reorder the terms:
15 + -13a + 6a2 = 6a

Solving
15 + -13a + 6a2 = 6a

Solving for variable 'a'.

Reorder the terms:
15 + -13a + -6a + 6a2 = 6a + -6a

Combine like terms: -13a + -6a = -19a
15 + -19a + 6a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
15 + -19a + 6a2 = 0

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

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

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a = 0 + -3
-2a = 0 + -3

Combine like terms: 0 + -3 = -3
-2a = -3

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve:

Simplifying
5 + -3a = 0

Solving
5 + -3a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3a = 0 + -5
-3a = 0 + -5

Combine like terms: 0 + -5 = -5
-3a = -5

Divide each side by '-3'.
a = 1.666666667

Simplifying
a = 1.666666667
Solution
a = {1.5, 1.666666667}