5(x+3)+x=4x(x+3)+3

Solution for 5(x+3)+x=4x(x+3)+3 equation:

Simplifying
5(x + 3) + x = 4x(x + 3) + 3

Reorder the terms:
5(3 + x) + x = 4x(x + 3) + 3
(3 * 5 + x * 5) + x = 4x(x + 3) + 3
(15 + 5x) + x = 4x(x + 3) + 3

Combine like terms: 5x + x = 6x
15 + 6x = 4x(x + 3) + 3

Reorder the terms:
15 + 6x = 4x(3 + x) + 3
15 + 6x = (3 * 4x + x * 4x) + 3
15 + 6x = (12x + 4x2) + 3

Reorder the terms:
15 + 6x = 3 + 12x + 4x2

Solving
15 + 6x = 3 + 12x + 4x2

Solving for variable 'x'.

Reorder the terms:
15 + -3 + 6x + -12x + -4x2 = 3 + 12x + 4x2 + -3 + -12x + -4x2

Combine like terms: 15 + -3 = 12
12 + 6x + -12x + -4x2 = 3 + 12x + 4x2 + -3 + -12x + -4x2

Combine like terms: 6x + -12x = -6x
12 + -6x + -4x2 = 3 + 12x + 4x2 + -3 + -12x + -4x2

Reorder the terms:
12 + -6x + -4x2 = 3 + -3 + 12x + -12x + 4x2 + -4x2

Combine like terms: 3 + -3 = 0
12 + -6x + -4x2 = 0 + 12x + -12x + 4x2 + -4x2
12 + -6x + -4x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
12 + -6x + -4x2 = 0 + 4x2 + -4x2
12 + -6x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + -6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -3x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -3x + -2x2)' equal to zero and attempt to solve:

Simplifying
6 + -3x + -2x2 = 0

Solving
6 + -3x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3 + 1.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 1.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 1.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1.5x + x2 = 0 + 3
1.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
1.5x + x2 = 3

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 3 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 3 + 0.5625

Combine like terms: 3 + 0.5625 = 3.5625
0.5625 + 1.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + 0.75) equal to 1.887458609 and -1.887458609.

Subproblem 1
x + 0.75 = 1.887458609

Simplifying
x + 0.75 = 1.887458609

Reorder the terms:
0.75 + x = 1.887458609

Solving
0.75 + x = 1.887458609

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 1.887458609 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 1.887458609 + -0.75
x = 1.887458609 + -0.75

Combine like terms: 1.887458609 + -0.75 = 1.137458609
x = 1.137458609

Simplifying
x = 1.137458609

Subproblem 2
x + 0.75 = -1.887458609

Simplifying
x + 0.75 = -1.887458609

Reorder the terms:
0.75 + x = -1.887458609

Solving
0.75 + x = -1.887458609

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -1.887458609 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -1.887458609 + -0.75
x = -1.887458609 + -0.75

Combine like terms: -1.887458609 + -0.75 = -2.637458609
x = -2.637458609

Simplifying
x = -2.637458609

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.137458609, -2.637458609}
Solution
x = {1.137458609, -2.637458609}