5x(6x+4)+4=16

Solution for 5x(6x+4)+4=16 equation:

Simplifying
5x(6x + 4) + 4 = 16

Reorder the terms:
5x(4 + 6x) + 4 = 16
(4 * 5x + 6x * 5x) + 4 = 16
(20x + 30x2) + 4 = 16

Reorder the terms:
4 + 20x + 30x2 = 16

Solving
4 + 20x + 30x2 = 16

Solving for variable 'x'.

Reorder the terms:
4 + -16 + 20x + 30x2 = 16 + -16

Combine like terms: 4 + -16 = -12
-12 + 20x + 30x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-12 + 20x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 10x + 15x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 10x + 15x2)' equal to zero and attempt to solve:

Simplifying
-6 + 10x + 15x2 = 0

Solving
-6 + 10x + 15x2 = 0

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

Divide each side by '15'.
-0.4 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.6666666667x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.6666666667x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.6666666667x + x2 = 0 + 0.4
0.6666666667x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.6666666667x + x2 = 0.4

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 0.4 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.4 + 0.1111111112

Combine like terms: 0.4 + 0.1111111112 = 0.5111111112
0.1111111112 + 0.6666666667x + x2 = 0.5111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.5111111112

Calculate the square root of the right side: 0.714920353

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.714920353 and -0.714920353.

Subproblem 1
x + 0.3333333334 = 0.714920353

Simplifying
x + 0.3333333334 = 0.714920353

Reorder the terms:
0.3333333334 + x = 0.714920353

Solving
0.3333333334 + x = 0.714920353

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.714920353 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.714920353 + -0.3333333334
x = 0.714920353 + -0.3333333334

Combine like terms: 0.714920353 + -0.3333333334 = 0.3815870196
x = 0.3815870196

Simplifying
x = 0.3815870196

Subproblem 2
x + 0.3333333334 = -0.714920353

Simplifying
x + 0.3333333334 = -0.714920353

Reorder the terms:
0.3333333334 + x = -0.714920353

Solving
0.3333333334 + x = -0.714920353

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.714920353 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.714920353 + -0.3333333334
x = -0.714920353 + -0.3333333334

Combine like terms: -0.714920353 + -0.3333333334 = -1.0482536864
x = -1.0482536864

Simplifying
x = -1.0482536864

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3815870196, -1.0482536864}
Solution
x = {0.3815870196, -1.0482536864}