2x^2+21x+27=500

Solution for 2x^2+21x+27=500 equation:

Simplifying
2x2 + 21x + 27 = 500

Reorder the terms:
27 + 21x + 2x2 = 500

Solving
27 + 21x + 2x2 = 500

Solving for variable 'x'.

Reorder the terms:
27 + -500 + 21x + 2x2 = 500 + -500

Combine like terms: 27 + -500 = -473
-473 + 21x + 2x2 = 500 + -500

Combine like terms: 500 + -500 = 0
-473 + 21x + 2x2 = 0

Factor a trinomial.
(-43 + -2x)(11 + -1x) = 0

Subproblem 1
Set the factor '(-43 + -2x)' equal to zero and attempt to solve:

Simplifying
-43 + -2x = 0

Solving
-43 + -2x = 0

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

Add '43' to each side of the equation.
-43 + 43 + -2x = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -2x = 0 + 43
-2x = 0 + 43

Combine like terms: 0 + 43 = 43
-2x = 43

Divide each side by '-2'.
x = -21.5

Simplifying
x = -21.5
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-21.5, 11}