5(3x^2-1)+16(3x-1)+3=0

Solution for 5(3x^2-1)+16(3x-1)+3=0 equation:

Simplifying
5(3x2 + -1) + 16(3x + -1) + 3 = 0

Reorder the terms:
5(-1 + 3x2) + 16(3x + -1) + 3 = 0
(-1 * 5 + 3x2 * 5) + 16(3x + -1) + 3 = 0
(-5 + 15x2) + 16(3x + -1) + 3 = 0

Reorder the terms:
-5 + 15x2 + 16(-1 + 3x) + 3 = 0
-5 + 15x2 + (-1 * 16 + 3x * 16) + 3 = 0
-5 + 15x2 + (-16 + 48x) + 3 = 0

Reorder the terms:
-5 + -16 + 3 + 48x + 15x2 = 0

Combine like terms: -5 + -16 = -21
-21 + 3 + 48x + 15x2 = 0

Combine like terms: -21 + 3 = -18
-18 + 48x + 15x2 = 0

Solving
-18 + 48x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 16x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + 16x + 5x2)' equal to zero and attempt to solve:

Simplifying
-6 + 16x + 5x2 = 0

Solving
-6 + 16x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + 3.2x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 3.2x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 3.2x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 3.2x + x2 = 0 + 1.2
3.2x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
3.2x + x2 = 1.2

The x term is 3.2x.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2x + 2.56 + x2 = 1.2 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = 1.2 + 2.56

Combine like terms: 1.2 + 2.56 = 3.76
2.56 + 3.2x + x2 = 3.76

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 3.76

Calculate the square root of the right side: 1.939071943

Break this problem into two subproblems by setting 
(x + 1.6) equal to 1.939071943 and -1.939071943.

Subproblem 1
x + 1.6 = 1.939071943

Simplifying
x + 1.6 = 1.939071943

Reorder the terms:
1.6 + x = 1.939071943

Solving
1.6 + x = 1.939071943

Solving for variable 'x'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + x = 1.939071943 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = 1.939071943 + -1.6
x = 1.939071943 + -1.6

Combine like terms: 1.939071943 + -1.6 = 0.339071943
x = 0.339071943

Simplifying
x = 0.339071943

Subproblem 2
x + 1.6 = -1.939071943

Simplifying
x + 1.6 = -1.939071943

Reorder the terms:
1.6 + x = -1.939071943

Solving
1.6 + x = -1.939071943

Solving for variable 'x'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + x = -1.939071943 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = -1.939071943 + -1.6
x = -1.939071943 + -1.6

Combine like terms: -1.939071943 + -1.6 = -3.539071943
x = -3.539071943

Simplifying
x = -3.539071943

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.339071943, -3.539071943}
Solution
x = {0.339071943, -3.539071943}