5a^2-13a=6

Solution for 5a^2-13a=6 equation:

Simplifying
5a2 + -13a = 6

Reorder the terms:
-13a + 5a2 = 6

Solving
-13a + 5a2 = 6

Solving for variable 'a'.

Reorder the terms:
-6 + -13a + 5a2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -13a + 5a2 = 0

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

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 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.4, 3}