35-17=3x(x-2)

Solution for 35-17=3x(x-2) equation:

Simplifying
35 + -17 = 3x(x + -2)

Combine like terms: 35 + -17 = 18
18 = 3x(x + -2)

Reorder the terms:
18 = 3x(-2 + x)
18 = (-2 * 3x + x * 3x)
18 = (-6x + 3x2)

Solving
18 = -6x + 3x2

Solving for variable 'x'.

Reorder the terms:
18 + 6x + -3x2 = -6x + 6x + 3x2 + -3x2

Combine like terms: -6x + 6x = 0
18 + 6x + -3x2 = 0 + 3x2 + -3x2
18 + 6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
18 + 6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 2x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + 2x + -1x2 = 0

Solving
6 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + -2x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -2x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2x + x2 = 0 + 6
-2x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2x + x2 = 6

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 6 + 1

Reorder the terms:
1 + -2x + x2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2x + x2 = 7

Factor a perfect square on the left side:
(x + -1)(x + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
x + -1 = 2.645751311

Simplifying
x + -1 = 2.645751311

Reorder the terms:
-1 + x = 2.645751311

Solving
-1 + x = 2.645751311

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.645751311 + 1
x = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
x = 3.645751311

Simplifying
x = 3.645751311

Subproblem 2
x + -1 = -2.645751311

Simplifying
x + -1 = -2.645751311

Reorder the terms:
-1 + x = -2.645751311

Solving
-1 + x = -2.645751311

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.645751311 + 1
x = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
x = -1.645751311

Simplifying
x = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.645751311, -1.645751311}
Solution
x = {3.645751311, -1.645751311}