6a^2+13a=5

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

Simplifying
6a2 + 13a = 5

Reorder the terms:
13a + 6a2 = 5

Solving
13a + 6a2 = 5

Solving for variable 'a'.

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

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

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

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

Simplifying
-5 + -2a = 0

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

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

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

Divide each side by '-2'.
a = -2.5

Simplifying
a = -2.5
Subproblem 2
Set the factor '(1 + -3a)' equal to zero and attempt to solve:

Simplifying
1 + -3a = 0

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

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

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

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Solution
a = {-2.5, 0.3333333333}