5x(3x+3)=3

Solution for 5x(3x+3)=3 equation:

Simplifying
5x(3x + 3) = 3

Reorder the terms:
5x(3 + 3x) = 3
(3 * 5x + 3x * 5x) = 3
(15x + 15x2) = 3

Solving
15x + 15x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 15x + 15x2 = 3 + -3

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

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 5x + 5x2) = 0

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

Simplifying
-1 + 5x + 5x2 = 0

Solving
-1 + 5x + 5x2 = 0

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

Divide each side by '5'.
-0.2 + x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x + x2 = 0 + 0.2
x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
x + x2 = 0.2

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.2 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.2 + 0.25

Combine like terms: 0.2 + 0.25 = 0.45
1.25 + x2 = 0.45

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.45

Calculate the square root of the right side: 0.670820393

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.670820393 and -0.670820393.

Subproblem 1
x + 0.5 = 0.670820393

Simplifying
x + 0.5 = 0.670820393

Reorder the terms:
0.5 + x = 0.670820393

Solving
0.5 + x = 0.670820393

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.670820393 + -0.5
x = 0.670820393 + -0.5

Combine like terms: 0.670820393 + -0.5 = 0.170820393
x = 0.170820393

Simplifying
x = 0.170820393

Subproblem 2
x + 0.5 = -0.670820393

Simplifying
x + 0.5 = -0.670820393

Reorder the terms:
0.5 + x = -0.670820393

Solving
0.5 + x = -0.670820393

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.670820393 + -0.5
x = -0.670820393 + -0.5

Combine like terms: -0.670820393 + -0.5 = -1.170820393
x = -1.170820393

Simplifying
x = -1.170820393

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.170820393, -1.170820393}
Solution
x = {0.170820393, -1.170820393}