a(a+6)=112

Solution for a(a+6)=112 equation:

Simplifying
a(a + 6) = 112

Reorder the terms:
a(6 + a) = 112
(6 * a + a * a) = 112
(6a + a2) = 112

Solving
6a + a2 = 112

Solving for variable 'a'.

Reorder the terms:
-112 + 6a + a2 = 112 + -112

Combine like terms: 112 + -112 = 0
-112 + 6a + a2 = 0

Factor a trinomial.
(-14 + -1a)(8 + -1a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {-14, 8}