a^2+3a-13=5

Solution for a^2+3a-13=5 equation:

Simplifying
a2 + 3a + -13 = 5

Reorder the terms:
-13 + 3a + a2 = 5

Solving
-13 + 3a + a2 = 5

Solving for variable 'a'.

Reorder the terms:
-13 + -5 + 3a + a2 = 5 + -5

Combine like terms: -13 + -5 = -18
-18 + 3a + a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-18 + 3a + a2 = 0

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

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

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 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 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
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 = {-6, 3}