24x=x^2+144

Solution for 24x=x^2+144 equation:

Simplifying
24x = x2 + 144

Reorder the terms:
24x = 144 + x2

Solving
24x = 144 + x2

Solving for variable 'x'.

Reorder the terms:
-144 + 24x + -1x2 = 144 + x2 + -144 + -1x2

Reorder the terms:
-144 + 24x + -1x2 = 144 + -144 + x2 + -1x2

Combine like terms: 144 + -144 = 0
-144 + 24x + -1x2 = 0 + x2 + -1x2
-144 + 24x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-144 + 24x + -1x2 = 0

Factor a trinomial.
(-12 + x)(12 + -1x) = 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 + -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}