(a+3)(a-4)=(a+12)

Solution for (a+3)(a-4)=(a+12) equation:

Simplifying
(a + 3)(a + -4) = (a + 12)

Reorder the terms:
(3 + a)(a + -4) = (a + 12)

Reorder the terms:
(3 + a)(-4 + a) = (a + 12)

Multiply (3 + a) * (-4 + a)
(3(-4 + a) + a(-4 + a)) = (a + 12)
((-4 * 3 + a * 3) + a(-4 + a)) = (a + 12)
((-12 + 3a) + a(-4 + a)) = (a + 12)
(-12 + 3a + (-4 * a + a * a)) = (a + 12)
(-12 + 3a + (-4a + a2)) = (a + 12)

Combine like terms: 3a + -4a = -1a
(-12 + -1a + a2) = (a + 12)

Reorder the terms:
-12 + -1a + a2 = (12 + a)

Remove parenthesis around (12 + a)
-12 + -1a + a2 = 12 + a

Solving
-12 + -1a + a2 = 12 + a

Solving for variable 'a'.

Reorder the terms:
-12 + -12 + -1a + -1a + a2 = 12 + a + -12 + -1a

Combine like terms: -12 + -12 = -24
-24 + -1a + -1a + a2 = 12 + a + -12 + -1a

Combine like terms: -1a + -1a = -2a
-24 + -2a + a2 = 12 + a + -12 + -1a

Reorder the terms:
-24 + -2a + a2 = 12 + -12 + a + -1a

Combine like terms: 12 + -12 = 0
-24 + -2a + a2 = 0 + a + -1a
-24 + -2a + a2 = a + -1a

Combine like terms: a + -1a = 0
-24 + -2a + a2 = 0

Factor a trinomial.
(-4 + -1a)(6 + -1a) = 0

Subproblem 1
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
Subproblem 2
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
Solution
a = {-4, 6}