5x(x+3)=3(x+9)

Solution for 5x(x+3)=3(x+9) equation:

Simplifying
5x(x + 3) = 3(x + 9)

Reorder the terms:
5x(3 + x) = 3(x + 9)
(3 * 5x + x * 5x) = 3(x + 9)
(15x + 5x2) = 3(x + 9)

Reorder the terms:
15x + 5x2 = 3(9 + x)
15x + 5x2 = (9 * 3 + x * 3)
15x + 5x2 = (27 + 3x)

Solving
15x + 5x2 = 27 + 3x

Solving for variable 'x'.

Reorder the terms:
-27 + 15x + -3x + 5x2 = 27 + 3x + -27 + -3x

Combine like terms: 15x + -3x = 12x
-27 + 12x + 5x2 = 27 + 3x + -27 + -3x

Reorder the terms:
-27 + 12x + 5x2 = 27 + -27 + 3x + -3x

Combine like terms: 27 + -27 = 0
-27 + 12x + 5x2 = 0 + 3x + -3x
-27 + 12x + 5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-27 + 12x + 5x2 = 0

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

Divide each side by '5'.
-5.4 + 2.4x + x2 = 0

Move the constant term to the right:

Add '5.4' to each side of the equation.
-5.4 + 2.4x + 5.4 + x2 = 0 + 5.4

Reorder the terms:
-5.4 + 5.4 + 2.4x + x2 = 0 + 5.4

Combine like terms: -5.4 + 5.4 = 0.0
0.0 + 2.4x + x2 = 0 + 5.4
2.4x + x2 = 0 + 5.4

Combine like terms: 0 + 5.4 = 5.4
2.4x + x2 = 5.4

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = 5.4 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 5.4 + 1.44

Combine like terms: 5.4 + 1.44 = 6.84
1.44 + 2.4x + x2 = 6.84

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 6.84

Calculate the square root of the right side: 2.615339366

Break this problem into two subproblems by setting 
(x + 1.2) equal to 2.615339366 and -2.615339366.

Subproblem 1
x + 1.2 = 2.615339366

Simplifying
x + 1.2 = 2.615339366

Reorder the terms:
1.2 + x = 2.615339366

Solving
1.2 + x = 2.615339366

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = 2.615339366 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = 2.615339366 + -1.2
x = 2.615339366 + -1.2

Combine like terms: 2.615339366 + -1.2 = 1.415339366
x = 1.415339366

Simplifying
x = 1.415339366

Subproblem 2
x + 1.2 = -2.615339366

Simplifying
x + 1.2 = -2.615339366

Reorder the terms:
1.2 + x = -2.615339366

Solving
1.2 + x = -2.615339366

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = -2.615339366 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = -2.615339366 + -1.2
x = -2.615339366 + -1.2

Combine like terms: -2.615339366 + -1.2 = -3.815339366
x = -3.815339366

Simplifying
x = -3.815339366

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.415339366, -3.815339366}