27x+x^2=1224

Solution for 27x+x^2=1224 equation:

Simplifying
27x + x2 = 1224

Solving
27x + x2 = 1224

Solving for variable 'x'.

Reorder the terms:
-1224 + 27x + x2 = 1224 + -1224

Combine like terms: 1224 + -1224 = 0
-1224 + 27x + x2 = 0

Factor a trinomial.
(-51 + -1x)(24 + -1x) = 0

Subproblem 1
Set the factor '(-51 + -1x)' equal to zero and attempt to solve:

Simplifying
-51 + -1x = 0

Solving
-51 + -1x = 0

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

Add '51' to each side of the equation.
-51 + 51 + -1x = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -1x = 0 + 51
-1x = 0 + 51

Combine like terms: 0 + 51 = 51
-1x = 51

Divide each side by '-1'.
x = -51

Simplifying
x = -51
Subproblem 2
Set the factor '(24 + -1x)' equal to zero and attempt to solve:

Simplifying
24 + -1x = 0

Solving
24 + -1x = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1x = 0 + -24

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

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

Divide each side by '-1'.
x = 24

Simplifying
x = 24
Solution
x = {-51, 24}