A*(A+24)=256

Solution for A*(A+24)=256 equation:

Simplifying
A(A + 24) = 256

Reorder the terms:
A(24 + A) = 256
(24 * A + A * A) = 256
(24A + A2) = 256

Solving
24A + A2 = 256

Solving for variable 'A'.

Reorder the terms:
-256 + 24A + A2 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + 24A + A2 = 0

Factor a trinomial.
(-32 + -1A)(8 + -1A) = 0

Subproblem 1
Set the factor '(-32 + -1A)' equal to zero and attempt to solve:

Simplifying
-32 + -1A = 0

Solving
-32 + -1A = 0

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

Add '32' to each side of the equation.
-32 + 32 + -1A = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1A = 0 + 32
-1A = 0 + 32

Combine like terms: 0 + 32 = 32
-1A = 32

Divide each side by '-1'.
A = -32

Simplifying
A = -32
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 = {-32, 8}