(6x-58)+(2x+4)5x=180

Solution for (6x-58)+(2x+4)5x=180 equation:

Simplifying
(6x + -58) + (2x + 4) * 5x = 180

Reorder the terms:
(-58 + 6x) + (2x + 4) * 5x = 180

Remove parenthesis around (-58 + 6x)
-58 + 6x + (2x + 4) * 5x = 180

Reorder the terms:
-58 + 6x + (4 + 2x) * 5x = 180

Reorder the terms for easier multiplication:
-58 + 6x + 5x(4 + 2x) = 180
-58 + 6x + (4 * 5x + 2x * 5x) = 180
-58 + 6x + (20x + 10x2) = 180

Combine like terms: 6x + 20x = 26x
-58 + 26x + 10x2 = 180

Solving
-58 + 26x + 10x2 = 180

Solving for variable 'x'.

Reorder the terms:
-58 + -180 + 26x + 10x2 = 180 + -180

Combine like terms: -58 + -180 = -238
-238 + 26x + 10x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-238 + 26x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-119 + 13x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-119 + 13x + 5x2)' equal to zero and attempt to solve:

Simplifying
-119 + 13x + 5x2 = 0

Solving
-119 + 13x + 5x2 = 0

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

Divide each side by '5'.
-23.8 + 2.6x + x2 = 0

Move the constant term to the right:

Add '23.8' to each side of the equation.
-23.8 + 2.6x + 23.8 + x2 = 0 + 23.8

Reorder the terms:
-23.8 + 23.8 + 2.6x + x2 = 0 + 23.8

Combine like terms: -23.8 + 23.8 = 0.0
0.0 + 2.6x + x2 = 0 + 23.8
2.6x + x2 = 0 + 23.8

Combine like terms: 0 + 23.8 = 23.8
2.6x + x2 = 23.8

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = 23.8 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = 23.8 + 1.69

Combine like terms: 23.8 + 1.69 = 25.49
1.69 + 2.6x + x2 = 25.49

Factor a perfect square on the left side:
(x + 1.3)(x + 1.3) = 25.49

Calculate the square root of the right side: 5.048762225

Break this problem into two subproblems by setting 
(x + 1.3) equal to 5.048762225 and -5.048762225.

Subproblem 1
x + 1.3 = 5.048762225

Simplifying
x + 1.3 = 5.048762225

Reorder the terms:
1.3 + x = 5.048762225

Solving
1.3 + x = 5.048762225

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = 5.048762225 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = 5.048762225 + -1.3
x = 5.048762225 + -1.3

Combine like terms: 5.048762225 + -1.3 = 3.748762225
x = 3.748762225

Simplifying
x = 3.748762225

Subproblem 2
x + 1.3 = -5.048762225

Simplifying
x + 1.3 = -5.048762225

Reorder the terms:
1.3 + x = -5.048762225

Solving
1.3 + x = -5.048762225

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = -5.048762225 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = -5.048762225 + -1.3
x = -5.048762225 + -1.3

Combine like terms: -5.048762225 + -1.3 = -6.348762225
x = -6.348762225

Simplifying
x = -6.348762225

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.748762225, -6.348762225}
Solution
x = {3.748762225, -6.348762225}