5(x-2)+x=6(x+3)4x

Solution for 5(x-2)+x=6(x+3)4x equation:

Simplifying
5(x + -2) + x = 6(x + 3) * 4x

Reorder the terms:
5(-2 + x) + x = 6(x + 3) * 4x
(-2 * 5 + x * 5) + x = 6(x + 3) * 4x
(-10 + 5x) + x = 6(x + 3) * 4x

Combine like terms: 5x + x = 6x
-10 + 6x = 6(x + 3) * 4x

Reorder the terms:
-10 + 6x = 6(3 + x) * 4x

Reorder the terms for easier multiplication:
-10 + 6x = 6 * 4x(3 + x)

Multiply 6 * 4
-10 + 6x = 24x(3 + x)
-10 + 6x = (3 * 24x + x * 24x)
-10 + 6x = (72x + 24x2)

Solving
-10 + 6x = 72x + 24x2

Solving for variable 'x'.

Combine like terms: 6x + -72x = -66x
-10 + -66x + -24x2 = 72x + 24x2 + -72x + -24x2

Reorder the terms:
-10 + -66x + -24x2 = 72x + -72x + 24x2 + -24x2

Combine like terms: 72x + -72x = 0
-10 + -66x + -24x2 = 0 + 24x2 + -24x2
-10 + -66x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
-10 + -66x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(5 + 33x + 12x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(5 + 33x + 12x2)' equal to zero and attempt to solve:

Simplifying
5 + 33x + 12x2 = 0

Solving
5 + 33x + 12x2 = 0

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

Divide each side by '12'.
0.4166666667 + 2.75x + x2 = 0

Move the constant term to the right:

Add '-0.4166666667' to each side of the equation.
0.4166666667 + 2.75x + -0.4166666667 + x2 = 0 + -0.4166666667

Reorder the terms:
0.4166666667 + -0.4166666667 + 2.75x + x2 = 0 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + 2.75x + x2 = 0 + -0.4166666667
2.75x + x2 = 0 + -0.4166666667

Combine like terms: 0 + -0.4166666667 = -0.4166666667
2.75x + x2 = -0.4166666667

The x term is 2.75x.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75x + 1.890625 + x2 = -0.4166666667 + 1.890625

Reorder the terms:
1.890625 + 2.75x + x2 = -0.4166666667 + 1.890625

Combine like terms: -0.4166666667 + 1.890625 = 1.4739583333
1.890625 + 2.75x + x2 = 1.4739583333

Factor a perfect square on the left side:
(x + 1.375)(x + 1.375) = 1.4739583333

Calculate the square root of the right side: 1.214066857

Break this problem into two subproblems by setting 
(x + 1.375) equal to 1.214066857 and -1.214066857.

Subproblem 1
x + 1.375 = 1.214066857

Simplifying
x + 1.375 = 1.214066857

Reorder the terms:
1.375 + x = 1.214066857

Solving
1.375 + x = 1.214066857

Solving for variable 'x'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + x = 1.214066857 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = 1.214066857 + -1.375
x = 1.214066857 + -1.375

Combine like terms: 1.214066857 + -1.375 = -0.160933143
x = -0.160933143

Simplifying
x = -0.160933143

Subproblem 2
x + 1.375 = -1.214066857

Simplifying
x + 1.375 = -1.214066857

Reorder the terms:
1.375 + x = -1.214066857

Solving
1.375 + x = -1.214066857

Solving for variable 'x'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + x = -1.214066857 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = -1.214066857 + -1.375
x = -1.214066857 + -1.375

Combine like terms: -1.214066857 + -1.375 = -2.589066857
x = -2.589066857

Simplifying
x = -2.589066857

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.160933143, -2.589066857}
Solution
x = {-0.160933143, -2.589066857}