5(4x+1)(3x)=27

Solution for 5(4x+1)(3x)=27 equation:

Simplifying
5(4x + 1)(3x) = 27

Reorder the terms:
5(1 + 4x)(3x) = 27

Remove parenthesis around (3x)
5(1 + 4x) * 3x = 27

Reorder the terms for easier multiplication:
5 * 3x(1 + 4x) = 27

Multiply 5 * 3
15x(1 + 4x) = 27
(1 * 15x + 4x * 15x) = 27
(15x + 60x2) = 27

Solving
15x + 60x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + 15x + 60x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 15x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 5x + 20x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-9 + 5x + 20x2)' equal to zero and attempt to solve:

Simplifying
-9 + 5x + 20x2 = 0

Solving
-9 + 5x + 20x2 = 0

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

Divide each side by '20'.
-0.45 + 0.25x + x2 = 0.0

Move the constant term to the right:

Add '0.45' to each side of the equation.
-0.45 + 0.25x + 0.45 + x2 = 0.0 + 0.45

Reorder the terms:
-0.45 + 0.45 + 0.25x + x2 = 0.0 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + 0.25x + x2 = 0.0 + 0.45
0.25x + x2 = 0.0 + 0.45

Combine like terms: 0.0 + 0.45 = 0.45
0.25x + x2 = 0.45

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 0.45 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.45 + 0.015625

Combine like terms: 0.45 + 0.015625 = 0.465625
0.015625 + 0.25x + x2 = 0.465625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.465625

Calculate the square root of the right side: 0.682367203

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.682367203 and -0.682367203.

Subproblem 1
x + 0.125 = 0.682367203

Simplifying
x + 0.125 = 0.682367203

Reorder the terms:
0.125 + x = 0.682367203

Solving
0.125 + x = 0.682367203

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 0.682367203 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 0.682367203 + -0.125
x = 0.682367203 + -0.125

Combine like terms: 0.682367203 + -0.125 = 0.557367203
x = 0.557367203

Simplifying
x = 0.557367203

Subproblem 2
x + 0.125 = -0.682367203

Simplifying
x + 0.125 = -0.682367203

Reorder the terms:
0.125 + x = -0.682367203

Solving
0.125 + x = -0.682367203

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -0.682367203 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -0.682367203 + -0.125
x = -0.682367203 + -0.125

Combine like terms: -0.682367203 + -0.125 = -0.807367203
x = -0.807367203

Simplifying
x = -0.807367203

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.557367203, -0.807367203}
Solution
x = {0.557367203, -0.807367203}