3x(6x-17)=x^2-34

Solution for 3x(6x-17)=x^2-34 equation:

Simplifying
3x(6x + -17) = x2 + -34

Reorder the terms:
3x(-17 + 6x) = x2 + -34
(-17 * 3x + 6x * 3x) = x2 + -34
(-51x + 18x2) = x2 + -34

Reorder the terms:
-51x + 18x2 = -34 + x2

Solving
-51x + 18x2 = -34 + x2

Solving for variable 'x'.

Reorder the terms:
34 + -51x + 18x2 + -1x2 = -34 + x2 + 34 + -1x2

Combine like terms: 18x2 + -1x2 = 17x2
34 + -51x + 17x2 = -34 + x2 + 34 + -1x2

Reorder the terms:
34 + -51x + 17x2 = -34 + 34 + x2 + -1x2

Combine like terms: -34 + 34 = 0
34 + -51x + 17x2 = 0 + x2 + -1x2
34 + -51x + 17x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
34 + -51x + 17x2 = 0

Factor out the Greatest Common Factor (GCF), '17'.
17(2 + -3x + x2) = 0

Factor a trinomial.
17((1 + -1x)(2 + -1x)) = 0

Ignore the factor 17.
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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}