a^2-13a=14

Solution for a^2-13a=14 equation:

Simplifying
a2 + -13a = 14

Reorder the terms:
-13a + a2 = 14

Solving
-13a + a2 = 14

Solving for variable 'a'.

Reorder the terms:
-14 + -13a + a2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -13a + a2 = 0

Factor a trinomial.
(-1 + -1a)(14 + -1a) = 0

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

Simplifying
-1 + -1a = 0

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

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

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

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

Simplifying
a = -1
Subproblem 2
Set the factor '(14 + -1a)' equal to zero and attempt to solve:

Simplifying
14 + -1a = 0

Solving
14 + -1a = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1a = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1a = 0 + -14
-1a = 0 + -14

Combine like terms: 0 + -14 = -14
-1a = -14

Divide each side by '-1'.
a = 14

Simplifying
a = 14
Solution
a = {-1, 14}