a^2+12a-7=6

Solution for a^2+12a-7=6 equation:

Simplifying
a2 + 12a + -7 = 6

Reorder the terms:
-7 + 12a + a2 = 6

Solving
-7 + 12a + a2 = 6

Solving for variable 'a'.

Reorder the terms:
-7 + -6 + 12a + a2 = 6 + -6

Combine like terms: -7 + -6 = -13
-13 + 12a + a2 = 6 + -6

Combine like terms: 6 + -6 = 0
-13 + 12a + a2 = 0

Factor a trinomial.
(-13 + -1a)(1 + -1a) = 0

Subproblem 1
Set the factor '(-13 + -1a)' equal to zero and attempt to solve:

Simplifying
-13 + -1a = 0

Solving
-13 + -1a = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1a = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1a = 0 + 13
-1a = 0 + 13

Combine like terms: 0 + 13 = 13
-1a = 13

Divide each side by '-1'.
a = -13

Simplifying
a = -13
Subproblem 2
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
Solution
a = {-13, 1}