(2-7i)x(9+5i)=x

Solution for (2-7i)x(9+5i)=x equation:

Simplifying
(2 + -7i) * x(9 + 5i) = x

Reorder the terms for easier multiplication:
x(2 + -7i)(9 + 5i) = x

Multiply (2 + -7i) * (9 + 5i)
x(2(9 + 5i) + -7i * (9 + 5i)) = x
x((9 * 2 + 5i * 2) + -7i * (9 + 5i)) = x
x((18 + 10i) + -7i * (9 + 5i)) = x
x(18 + 10i + (9 * -7i + 5i * -7i)) = x
x(18 + 10i + (-63i + -35i2)) = x

Combine like terms: 10i + -63i = -53i
x(18 + -53i + -35i2) = x
(18 * x + -53i * x + -35i2 * x) = x

Reorder the terms:
(-53ix + -35i2x + 18x) = x
(-53ix + -35i2x + 18x) = x

Solving
-53ix + -35i2x + 18x = x

Solving for variable 'i'.

Combine like terms: 18x + -1x = 17x
-53ix + -35i2x + 17x = x + -1x

Combine like terms: x + -1x = 0
-53ix + -35i2x + 17x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-53i + -35i2 + 17) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

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

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-53i + -35i2 + 17)' equal to zero and attempt to solve:

Simplifying
-53i + -35i2 + 17 = 0

Reorder the terms:
17 + -53i + -35i2 = 0

Solving
17 + -53i + -35i2 = 0

Begin completing the square.  Divide all terms by
-35 the coefficient of the squared term: 

Divide each side by '-35'.
-0.4857142857 + 1.514285714i + i2 = 0

Move the constant term to the right:

Add '0.4857142857' to each side of the equation.
-0.4857142857 + 1.514285714i + 0.4857142857 + i2 = 0 + 0.4857142857

Reorder the terms:
-0.4857142857 + 0.4857142857 + 1.514285714i + i2 = 0 + 0.4857142857

Combine like terms: -0.4857142857 + 0.4857142857 = 0.0000000000
0.0000000000 + 1.514285714i + i2 = 0 + 0.4857142857
1.514285714i + i2 = 0 + 0.4857142857

Combine like terms: 0 + 0.4857142857 = 0.4857142857
1.514285714i + i2 = 0.4857142857

The i term is 1.514285714i.  Take half its coefficient (0.757142857).
Square it (0.5732653059) and add it to both sides.

Add '0.5732653059' to each side of the equation.
1.514285714i + 0.5732653059 + i2 = 0.4857142857 + 0.5732653059

Reorder the terms:
0.5732653059 + 1.514285714i + i2 = 0.4857142857 + 0.5732653059

Combine like terms: 0.4857142857 + 0.5732653059 = 1.0589795916
0.5732653059 + 1.514285714i + i2 = 1.0589795916

Factor a perfect square on the left side:
(i + 0.757142857)(i + 0.757142857) = 1.0589795916

Calculate the square root of the right side: 1.029067341

Break this problem into two subproblems by setting 
(i + 0.757142857) equal to 1.029067341 and -1.029067341.

Subproblem 1
i + 0.757142857 = 1.029067341

Simplifying
i + 0.757142857 = 1.029067341

Reorder the terms:
0.757142857 + i = 1.029067341

Solving
0.757142857 + i = 1.029067341

Solving for variable 'i'.

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

Add '-0.757142857' to each side of the equation.
0.757142857 + -0.757142857 + i = 1.029067341 + -0.757142857

Combine like terms: 0.757142857 + -0.757142857 = 0.000000000
0.000000000 + i = 1.029067341 + -0.757142857
i = 1.029067341 + -0.757142857

Combine like terms: 1.029067341 + -0.757142857 = 0.271924484
i = 0.271924484

Simplifying
i = 0.271924484

Subproblem 2
i + 0.757142857 = -1.029067341

Simplifying
i + 0.757142857 = -1.029067341

Reorder the terms:
0.757142857 + i = -1.029067341

Solving
0.757142857 + i = -1.029067341

Solving for variable 'i'.

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

Add '-0.757142857' to each side of the equation.
0.757142857 + -0.757142857 + i = -1.029067341 + -0.757142857

Combine like terms: 0.757142857 + -0.757142857 = 0.000000000
0.000000000 + i = -1.029067341 + -0.757142857
i = -1.029067341 + -0.757142857

Combine like terms: -1.029067341 + -0.757142857 = -1.786210198
i = -1.786210198

Simplifying
i = -1.786210198

Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {0.271924484, -1.786210198}
Solution
i = {0.271924484, -1.786210198}