48=15+6(4+x)3x

Solution for 48=15+6(4+x)3x equation:

Simplifying
48 = 15 + 6(4 + x) * 3x

Reorder the terms for easier multiplication:
48 = 15 + 6 * 3x(4 + x)

Multiply 6 * 3
48 = 15 + 18x(4 + x)
48 = 15 + (4 * 18x + x * 18x)
48 = 15 + (72x + 18x2)

Solving
48 = 15 + 72x + 18x2

Solving for variable 'x'.

Combine like terms: 48 + -15 = 33
33 + -72x + -18x2 = 15 + 72x + 18x2 + -15 + -72x + -18x2

Reorder the terms:
33 + -72x + -18x2 = 15 + -15 + 72x + -72x + 18x2 + -18x2

Combine like terms: 15 + -15 = 0
33 + -72x + -18x2 = 0 + 72x + -72x + 18x2 + -18x2
33 + -72x + -18x2 = 72x + -72x + 18x2 + -18x2

Combine like terms: 72x + -72x = 0
33 + -72x + -18x2 = 0 + 18x2 + -18x2
33 + -72x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
33 + -72x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(11 + -24x + -6x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(11 + -24x + -6x2)' equal to zero and attempt to solve:

Simplifying
11 + -24x + -6x2 = 0

Solving
11 + -24x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1.833333333 + 4x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + 4x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + 4x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + 4x + x2 = 0 + 1.833333333
4x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
4x + x2 = 1.833333333

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 1.833333333 + 4

Reorder the terms:
4 + 4x + x2 = 1.833333333 + 4

Combine like terms: 1.833333333 + 4 = 5.833333333
4 + 4x + x2 = 5.833333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5.833333333

Calculate the square root of the right side: 2.415229458

Break this problem into two subproblems by setting 
(x + 2) equal to 2.415229458 and -2.415229458.

Subproblem 1
x + 2 = 2.415229458

Simplifying
x + 2 = 2.415229458

Reorder the terms:
2 + x = 2.415229458

Solving
2 + x = 2.415229458

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.415229458 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.415229458 + -2
x = 2.415229458 + -2

Combine like terms: 2.415229458 + -2 = 0.415229458
x = 0.415229458

Simplifying
x = 0.415229458

Subproblem 2
x + 2 = -2.415229458

Simplifying
x + 2 = -2.415229458

Reorder the terms:
2 + x = -2.415229458

Solving
2 + x = -2.415229458

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.415229458 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.415229458 + -2
x = -2.415229458 + -2

Combine like terms: -2.415229458 + -2 = -4.415229458
x = -4.415229458

Simplifying
x = -4.415229458

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.415229458, -4.415229458}
Solution
x = {0.415229458, -4.415229458}