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

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

Simplifying
4x(5 + 3x) = 5(x + 3)
(5 * 4x + 3x * 4x) = 5(x + 3)
(20x + 12x2) = 5(x + 3)

Reorder the terms:
20x + 12x2 = 5(3 + x)
20x + 12x2 = (3 * 5 + x * 5)
20x + 12x2 = (15 + 5x)

Solving
20x + 12x2 = 15 + 5x

Solving for variable 'x'.

Reorder the terms:
-15 + 20x + -5x + 12x2 = 15 + 5x + -15 + -5x

Combine like terms: 20x + -5x = 15x
-15 + 15x + 12x2 = 15 + 5x + -15 + -5x

Reorder the terms:
-15 + 15x + 12x2 = 15 + -15 + 5x + -5x

Combine like terms: 15 + -15 = 0
-15 + 15x + 12x2 = 0 + 5x + -5x
-15 + 15x + 12x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-15 + 15x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 5x + 4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + 5x + 4x2)' equal to zero and attempt to solve:

Simplifying
-5 + 5x + 4x2 = 0

Solving
-5 + 5x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + 1.25x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 1.25x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 1.25x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 1.25x + x2 = 0 + 1.25
1.25x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
1.25x + x2 = 1.25

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 1.25 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 1.25 + 0.390625

Combine like terms: 1.25 + 0.390625 = 1.640625
0.390625 + 1.25x + x2 = 1.640625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 1.640625

Calculate the square root of the right side: 1.280868846

Break this problem into two subproblems by setting 
(x + 0.625) equal to 1.280868846 and -1.280868846.

Subproblem 1
x + 0.625 = 1.280868846

Simplifying
x + 0.625 = 1.280868846

Reorder the terms:
0.625 + x = 1.280868846

Solving
0.625 + x = 1.280868846

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 1.280868846 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 1.280868846 + -0.625
x = 1.280868846 + -0.625

Combine like terms: 1.280868846 + -0.625 = 0.655868846
x = 0.655868846

Simplifying
x = 0.655868846

Subproblem 2
x + 0.625 = -1.280868846

Simplifying
x + 0.625 = -1.280868846

Reorder the terms:
0.625 + x = -1.280868846

Solving
0.625 + x = -1.280868846

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -1.280868846 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -1.280868846 + -0.625
x = -1.280868846 + -0.625

Combine like terms: -1.280868846 + -0.625 = -1.905868846
x = -1.905868846

Simplifying
x = -1.905868846

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.655868846, -1.905868846}
Solution
x = {0.655868846, -1.905868846}