x(x-24)=-48(x+3)

Solution for x(x-24)=-48(x+3) equation:

Simplifying
x(x + -24) = -48(x + 3)

Reorder the terms:
x(-24 + x) = -48(x + 3)
(-24 * x + x * x) = -48(x + 3)
(-24x + x2) = -48(x + 3)

Reorder the terms:
-24x + x2 = -48(3 + x)
-24x + x2 = (3 * -48 + x * -48)
-24x + x2 = (-144 + -48x)

Solving
-24x + x2 = -144 + -48x

Solving for variable 'x'.

Reorder the terms:
144 + -24x + 48x + x2 = -144 + -48x + 144 + 48x

Combine like terms: -24x + 48x = 24x
144 + 24x + x2 = -144 + -48x + 144 + 48x

Reorder the terms:
144 + 24x + x2 = -144 + 144 + -48x + 48x

Combine like terms: -144 + 144 = 0
144 + 24x + x2 = 0 + -48x + 48x
144 + 24x + x2 = -48x + 48x

Combine like terms: -48x + 48x = 0
144 + 24x + x2 = 0

Factor a trinomial.
(12 + x)(12 + x) = 0

Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {-12, -12}