5(x+10)2x=246

Solution for 5(x+10)2x=246 equation:

Simplifying
5(x + 10) * 2x = 246

Reorder the terms:
5(10 + x) * 2x = 246

Reorder the terms for easier multiplication:
5 * 2x(10 + x) = 246

Multiply 5 * 2
10x(10 + x) = 246
(10 * 10x + x * 10x) = 246
(100x + 10x2) = 246

Solving
100x + 10x2 = 246

Solving for variable 'x'.

Reorder the terms:
-246 + 100x + 10x2 = 246 + -246

Combine like terms: 246 + -246 = 0
-246 + 100x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-123 + 50x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-123 + 50x + 5x2)' equal to zero and attempt to solve:

Simplifying
-123 + 50x + 5x2 = 0

Solving
-123 + 50x + 5x2 = 0

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

Divide each side by '5'.
-24.6 + 10x + x2 = 0

Move the constant term to the right:

Add '24.6' to each side of the equation.
-24.6 + 10x + 24.6 + x2 = 0 + 24.6

Reorder the terms:
-24.6 + 24.6 + 10x + x2 = 0 + 24.6

Combine like terms: -24.6 + 24.6 = 0.0
0.0 + 10x + x2 = 0 + 24.6
10x + x2 = 0 + 24.6

Combine like terms: 0 + 24.6 = 24.6
10x + x2 = 24.6

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 24.6 + 25

Reorder the terms:
25 + 10x + x2 = 24.6 + 25

Combine like terms: 24.6 + 25 = 49.6
25 + 10x + x2 = 49.6

Factor a perfect square on the left side:
(x + 5)(x + 5) = 49.6

Calculate the square root of the right side: 7.042726745

Break this problem into two subproblems by setting 
(x + 5) equal to 7.042726745 and -7.042726745.

Subproblem 1
x + 5 = 7.042726745

Simplifying
x + 5 = 7.042726745

Reorder the terms:
5 + x = 7.042726745

Solving
5 + x = 7.042726745

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 7.042726745 + -5

Combine like terms: 5 + -5 = 0
0 + x = 7.042726745 + -5
x = 7.042726745 + -5

Combine like terms: 7.042726745 + -5 = 2.042726745
x = 2.042726745

Simplifying
x = 2.042726745

Subproblem 2
x + 5 = -7.042726745

Simplifying
x + 5 = -7.042726745

Reorder the terms:
5 + x = -7.042726745

Solving
5 + x = -7.042726745

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -7.042726745 + -5

Combine like terms: 5 + -5 = 0
0 + x = -7.042726745 + -5
x = -7.042726745 + -5

Combine like terms: -7.042726745 + -5 = -12.042726745
x = -12.042726745

Simplifying
x = -12.042726745

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.042726745, -12.042726745}
Solution
x = {2.042726745, -12.042726745}