a^2-6a+a^2+a-12=0

Solution for a^2-6a+a^2+a-12=0 equation:

Simplifying
a2 + -6a + a2 + a + -12 = 0

Reorder the terms:
-12 + -6a + a + a2 + a2 = 0

Combine like terms: -6a + a = -5a
-12 + -5a + a2 + a2 = 0

Combine like terms: a2 + a2 = 2a2
-12 + -5a + 2a2 = 0

Solving
-12 + -5a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -2a)(4 + -1a) = 0

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

Simplifying
-3 + -2a = 0

Solving
-3 + -2a = 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 + -2a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2a = 0 + 3
-2a = 0 + 3

Combine like terms: 0 + 3 = 3
-2a = 3

Divide each side by '-2'.
a = -1.5

Simplifying
a = -1.5
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-1.5, 4}