17(x^2-20x+84)=0

Solution for 17(x^2-20x+84)=0 equation:

Simplifying
17(x2 + -20x + 84) = 0

Reorder the terms:
17(84 + -20x + x2) = 0
(84 * 17 + -20x * 17 + x2 * 17) = 0
(1428 + -340x + 17x2) = 0

Solving
1428 + -340x + 17x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '17'.
17(84 + -20x + x2) = 0

Factor a trinomial.
17((6 + -1x)(14 + -1x)) = 0

Ignore the factor 17.
Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {6, 14}