4(3x+6)5x=26

Solution for 4(3x+6)5x=26 equation:

Simplifying
4(3x + 6) * 5x = 26

Reorder the terms:
4(6 + 3x) * 5x = 26

Reorder the terms for easier multiplication:
4 * 5x(6 + 3x) = 26

Multiply 4 * 5
20x(6 + 3x) = 26
(6 * 20x + 3x * 20x) = 26
(120x + 60x2) = 26

Solving
120x + 60x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + 120x + 60x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 120x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 60x + 30x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + 60x + 30x2)' equal to zero and attempt to solve:

Simplifying
-13 + 60x + 30x2 = 0

Solving
-13 + 60x + 30x2 = 0

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

Divide each side by '30'.
-0.4333333333 + 2x + x2 = 0.0

Move the constant term to the right:

Add '0.4333333333' to each side of the equation.
-0.4333333333 + 2x + 0.4333333333 + x2 = 0.0 + 0.4333333333

Reorder the terms:
-0.4333333333 + 0.4333333333 + 2x + x2 = 0.0 + 0.4333333333

Combine like terms: -0.4333333333 + 0.4333333333 = 0.0000000000
0.0000000000 + 2x + x2 = 0.0 + 0.4333333333
2x + x2 = 0.0 + 0.4333333333

Combine like terms: 0.0 + 0.4333333333 = 0.4333333333
2x + x2 = 0.4333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 0.4333333333 + 1

Reorder the terms:
1 + 2x + x2 = 0.4333333333 + 1

Combine like terms: 0.4333333333 + 1 = 1.4333333333
1 + 2x + x2 = 1.4333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.4333333333

Calculate the square root of the right side: 1.197219

Break this problem into two subproblems by setting 
(x + 1) equal to 1.197219 and -1.197219.

Subproblem 1
x + 1 = 1.197219

Simplifying
x + 1 = 1.197219

Reorder the terms:
1 + x = 1.197219

Solving
1 + x = 1.197219

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.197219 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.197219 + -1
x = 1.197219 + -1

Combine like terms: 1.197219 + -1 = 0.197219
x = 0.197219

Simplifying
x = 0.197219

Subproblem 2
x + 1 = -1.197219

Simplifying
x + 1 = -1.197219

Reorder the terms:
1 + x = -1.197219

Solving
1 + x = -1.197219

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.197219 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.197219 + -1
x = -1.197219 + -1

Combine like terms: -1.197219 + -1 = -2.197219
x = -2.197219

Simplifying
x = -2.197219

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.197219, -2.197219}
Solution
x = {0.197219, -2.197219}