(9x-4)*-7(-9x+2)=17

Solution for (9x-4)*-7(-9x+2)=17 equation:

Simplifying
(9x + -4) * -7(-9x + 2) = 17

Reorder the terms:
(-4 + 9x) * -7(-9x + 2) = 17

Reorder the terms:
(-4 + 9x) * -7(2 + -9x) = 17

Reorder the terms for easier multiplication:
-7(-4 + 9x)(2 + -9x) = 17

Multiply (-4 + 9x) * (2 + -9x)
-7(-4(2 + -9x) + 9x * (2 + -9x)) = 17
-7((2 * -4 + -9x * -4) + 9x * (2 + -9x)) = 17
-7((-8 + 36x) + 9x * (2 + -9x)) = 17
-7(-8 + 36x + (2 * 9x + -9x * 9x)) = 17
-7(-8 + 36x + (18x + -81x2)) = 17

Combine like terms: 36x + 18x = 54x
-7(-8 + 54x + -81x2) = 17
(-8 * -7 + 54x * -7 + -81x2 * -7) = 17
(56 + -378x + 567x2) = 17

Solving
56 + -378x + 567x2 = 17

Solving for variable 'x'.

Reorder the terms:
56 + -17 + -378x + 567x2 = 17 + -17

Combine like terms: 56 + -17 = 39
39 + -378x + 567x2 = 17 + -17

Combine like terms: 17 + -17 = 0
39 + -378x + 567x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(13 + -126x + 189x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(13 + -126x + 189x2)' equal to zero and attempt to solve:

Simplifying
13 + -126x + 189x2 = 0

Solving
13 + -126x + 189x2 = 0

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

Divide each side by '189'.
0.06878306878 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-0.06878306878' to each side of the equation.
0.06878306878 + -0.6666666667x + -0.06878306878 + x2 = 0 + -0.06878306878

Reorder the terms:
0.06878306878 + -0.06878306878 + -0.6666666667x + x2 = 0 + -0.06878306878

Combine like terms: 0.06878306878 + -0.06878306878 = 0.00000000000
0.00000000000 + -0.6666666667x + x2 = 0 + -0.06878306878
-0.6666666667x + x2 = 0 + -0.06878306878

Combine like terms: 0 + -0.06878306878 = -0.06878306878
-0.6666666667x + x2 = -0.06878306878

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = -0.06878306878 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -0.06878306878 + 0.1111111112

Combine like terms: -0.06878306878 + 0.1111111112 = 0.04232804242
0.1111111112 + -0.6666666667x + x2 = 0.04232804242

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 0.04232804242

Calculate the square root of the right side: 0.2057378

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 0.2057378 and -0.2057378.

Subproblem 1
x + -0.3333333334 = 0.2057378

Simplifying
x + -0.3333333334 = 0.2057378

Reorder the terms:
-0.3333333334 + x = 0.2057378

Solving
-0.3333333334 + x = 0.2057378

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 0.2057378 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 0.2057378 + 0.3333333334
x = 0.2057378 + 0.3333333334

Combine like terms: 0.2057378 + 0.3333333334 = 0.5390711334
x = 0.5390711334

Simplifying
x = 0.5390711334

Subproblem 2
x + -0.3333333334 = -0.2057378

Simplifying
x + -0.3333333334 = -0.2057378

Reorder the terms:
-0.3333333334 + x = -0.2057378

Solving
-0.3333333334 + x = -0.2057378

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -0.2057378 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -0.2057378 + 0.3333333334
x = -0.2057378 + 0.3333333334

Combine like terms: -0.2057378 + 0.3333333334 = 0.1275955334
x = 0.1275955334

Simplifying
x = 0.1275955334

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5390711334, 0.1275955334}
Solution
x = {0.5390711334, 0.1275955334}