10x+26x(x-4)=184

Solution for 10x+26x(x-4)=184 equation:

Simplifying
10x + 26x(x + -4) = 184

Reorder the terms:
10x + 26x(-4 + x) = 184
10x + (-4 * 26x + x * 26x) = 184
10x + (-104x + 26x2) = 184

Combine like terms: 10x + -104x = -94x
-94x + 26x2 = 184

Solving
-94x + 26x2 = 184

Solving for variable 'x'.

Reorder the terms:
-184 + -94x + 26x2 = 184 + -184

Combine like terms: 184 + -184 = 0
-184 + -94x + 26x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-92 + -47x + 13x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-92 + -47x + 13x2)' equal to zero and attempt to solve:

Simplifying
-92 + -47x + 13x2 = 0

Solving
-92 + -47x + 13x2 = 0

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

Divide each side by '13'.
-7.076923077 + -3.615384615x + x2 = 0

Move the constant term to the right:

Add '7.076923077' to each side of the equation.
-7.076923077 + -3.615384615x + 7.076923077 + x2 = 0 + 7.076923077

Reorder the terms:
-7.076923077 + 7.076923077 + -3.615384615x + x2 = 0 + 7.076923077

Combine like terms: -7.076923077 + 7.076923077 = 0.000000000
0.000000000 + -3.615384615x + x2 = 0 + 7.076923077
-3.615384615x + x2 = 0 + 7.076923077

Combine like terms: 0 + 7.076923077 = 7.076923077
-3.615384615x + x2 = 7.076923077

The x term is -3.615384615x.  Take half its coefficient (-1.807692308).
Square it (3.267751480) and add it to both sides.

Add '3.267751480' to each side of the equation.
-3.615384615x + 3.267751480 + x2 = 7.076923077 + 3.267751480

Reorder the terms:
3.267751480 + -3.615384615x + x2 = 7.076923077 + 3.267751480

Combine like terms: 7.076923077 + 3.267751480 = 10.344674557
3.267751480 + -3.615384615x + x2 = 10.344674557

Factor a perfect square on the left side:
(x + -1.807692308)(x + -1.807692308) = 10.344674557

Calculate the square root of the right side: 3.216313815

Break this problem into two subproblems by setting 
(x + -1.807692308) equal to 3.216313815 and -3.216313815.

Subproblem 1
x + -1.807692308 = 3.216313815

Simplifying
x + -1.807692308 = 3.216313815

Reorder the terms:
-1.807692308 + x = 3.216313815

Solving
-1.807692308 + x = 3.216313815

Solving for variable 'x'.

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

Add '1.807692308' to each side of the equation.
-1.807692308 + 1.807692308 + x = 3.216313815 + 1.807692308

Combine like terms: -1.807692308 + 1.807692308 = 0.000000000
0.000000000 + x = 3.216313815 + 1.807692308
x = 3.216313815 + 1.807692308

Combine like terms: 3.216313815 + 1.807692308 = 5.024006123
x = 5.024006123

Simplifying
x = 5.024006123

Subproblem 2
x + -1.807692308 = -3.216313815

Simplifying
x + -1.807692308 = -3.216313815

Reorder the terms:
-1.807692308 + x = -3.216313815

Solving
-1.807692308 + x = -3.216313815

Solving for variable 'x'.

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

Add '1.807692308' to each side of the equation.
-1.807692308 + 1.807692308 + x = -3.216313815 + 1.807692308

Combine like terms: -1.807692308 + 1.807692308 = 0.000000000
0.000000000 + x = -3.216313815 + 1.807692308
x = -3.216313815 + 1.807692308

Combine like terms: -3.216313815 + 1.807692308 = -1.408621507
x = -1.408621507

Simplifying
x = -1.408621507

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.024006123, -1.408621507}
Solution
x = {5.024006123, -1.408621507}