5(2x+6)x=4

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

Simplifying
5(2x + 6) * x = 4

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

Reorder the terms for easier multiplication:
5x(6 + 2x) = 4
(6 * 5x + 2x * 5x) = 4
(30x + 10x2) = 4

Solving
30x + 10x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 30x + 10x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 30x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 15x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + 15x + 5x2)' equal to zero and attempt to solve:

Simplifying
-2 + 15x + 5x2 = 0

Solving
-2 + 15x + 5x2 = 0

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

Divide each side by '5'.
-0.4 + 3x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 3x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 3x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 3x + x2 = 0 + 0.4
3x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
3x + x2 = 0.4

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 0.4 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.4 + 2.25

Combine like terms: 0.4 + 2.25 = 2.65
2.25 + 3x + x2 = 2.65

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.65

Calculate the square root of the right side: 1.62788206

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.62788206 and -1.62788206.

Subproblem 1
x + 1.5 = 1.62788206

Simplifying
x + 1.5 = 1.62788206

Reorder the terms:
1.5 + x = 1.62788206

Solving
1.5 + x = 1.62788206

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.62788206 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.62788206 + -1.5
x = 1.62788206 + -1.5

Combine like terms: 1.62788206 + -1.5 = 0.12788206
x = 0.12788206

Simplifying
x = 0.12788206

Subproblem 2
x + 1.5 = -1.62788206

Simplifying
x + 1.5 = -1.62788206

Reorder the terms:
1.5 + x = -1.62788206

Solving
1.5 + x = -1.62788206

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.62788206 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.62788206 + -1.5
x = -1.62788206 + -1.5

Combine like terms: -1.62788206 + -1.5 = -3.12788206
x = -3.12788206

Simplifying
x = -3.12788206

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.12788206, -3.12788206}
Solution
x = {0.12788206, -3.12788206}