a^2-4a=3a-12

Solution for a^2-4a=3a-12 equation:

Simplifying
a2 + -4a = 3a + -12

Reorder the terms:
-4a + a2 = 3a + -12

Reorder the terms:
-4a + a2 = -12 + 3a

Solving
-4a + a2 = -12 + 3a

Solving for variable 'a'.

Reorder the terms:
12 + -4a + -3a + a2 = -12 + 3a + 12 + -3a

Combine like terms: -4a + -3a = -7a
12 + -7a + a2 = -12 + 3a + 12 + -3a

Reorder the terms:
12 + -7a + a2 = -12 + 12 + 3a + -3a

Combine like terms: -12 + 12 = 0
12 + -7a + a2 = 0 + 3a + -3a
12 + -7a + a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
12 + -7a + a2 = 0

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

Subproblem 1
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
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 = {3, 4}