x^2+27x+182=462

Solution for x^2+27x+182=462 equation:

Simplifying
x2 + 27x + 182 = 462

Reorder the terms:
182 + 27x + x2 = 462

Solving
182 + 27x + x2 = 462

Solving for variable 'x'.

Reorder the terms:
182 + -462 + 27x + x2 = 462 + -462

Combine like terms: 182 + -462 = -280
-280 + 27x + x2 = 462 + -462

Combine like terms: 462 + -462 = 0
-280 + 27x + x2 = 0

Factor a trinomial.
(-35 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-35 + -1x)' equal to zero and attempt to solve:

Simplifying
-35 + -1x = 0

Solving
-35 + -1x = 0

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

Add '35' to each side of the equation.
-35 + 35 + -1x = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -1x = 0 + 35
-1x = 0 + 35

Combine like terms: 0 + 35 = 35
-1x = 35

Divide each side by '-1'.
x = -35

Simplifying
x = -35
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-35, 8}