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 + -1x)(12 + -1x) = 0

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

Simplifying
12 + -1x = 0

Solving
12 + -1x = 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 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 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 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

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