x^2+32x=1024-256

Solution for x^2+32x=1024-256 equation:

Simplifying
x2 + 32x = 1024 + -256

Reorder the terms:
32x + x2 = 1024 + -256

Combine like terms: 1024 + -256 = 768
32x + x2 = 768

Solving
32x + x2 = 768

Solving for variable 'x'.

Reorder the terms:
-768 + 32x + x2 = 768 + -768

Combine like terms: 768 + -768 = 0
-768 + 32x + x2 = 0

Factor a trinomial.
(-48 + -1x)(16 + -1x) = 0

Subproblem 1
Set the factor '(-48 + -1x)' equal to zero and attempt to solve:

Simplifying
-48 + -1x = 0

Solving
-48 + -1x = 0

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

Add '48' to each side of the equation.
-48 + 48 + -1x = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -1x = 0 + 48
-1x = 0 + 48

Combine like terms: 0 + 48 = 48
-1x = 48

Divide each side by '-1'.
x = -48

Simplifying
x = -48
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-48, 16}