2x^2-21x-6=17

Solution for 2x^2-21x-6=17 equation:

Simplifying
2x2 + -21x + -6 = 17

Reorder the terms:
-6 + -21x + 2x2 = 17

Solving
-6 + -21x + 2x2 = 17

Solving for variable 'x'.

Reorder the terms:
-6 + -17 + -21x + 2x2 = 17 + -17

Combine like terms: -6 + -17 = -23
-23 + -21x + 2x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-23 + -21x + 2x2 = 0

Factor a trinomial.
(-1 + -1x)(23 + -2x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(23 + -2x)' equal to zero and attempt to solve:

Simplifying
23 + -2x = 0

Solving
23 + -2x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -2x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -2x = 0 + -23
-2x = 0 + -23

Combine like terms: 0 + -23 = -23
-2x = -23

Divide each side by '-2'.
x = 11.5

Simplifying
x = 11.5
Solution
x = {-1, 11.5}