4(2X+1)3(X-2)=10+5X

Solution for 4(2X+1)3(X-2)=10+5X equation:

Simplifying
4(2X + 1) * 3(X + -2) = 10 + 5X

Reorder the terms:
4(1 + 2X) * 3(X + -2) = 10 + 5X

Reorder the terms:
4(1 + 2X) * 3(-2 + X) = 10 + 5X

Reorder the terms for easier multiplication:
4 * 3(1 + 2X)(-2 + X) = 10 + 5X

Multiply 4 * 3
12(1 + 2X)(-2 + X) = 10 + 5X

Multiply (1 + 2X) * (-2 + X)
12(1(-2 + X) + 2X * (-2 + X)) = 10 + 5X
12((-2 * 1 + X * 1) + 2X * (-2 + X)) = 10 + 5X
12((-2 + 1X) + 2X * (-2 + X)) = 10 + 5X
12(-2 + 1X + (-2 * 2X + X * 2X)) = 10 + 5X
12(-2 + 1X + (-4X + 2X2)) = 10 + 5X

Combine like terms: 1X + -4X = -3X
12(-2 + -3X + 2X2) = 10 + 5X
(-2 * 12 + -3X * 12 + 2X2 * 12) = 10 + 5X
(-24 + -36X + 24X2) = 10 + 5X

Solving
-24 + -36X + 24X2 = 10 + 5X

Solving for variable 'X'.

Reorder the terms:
-24 + -10 + -36X + -5X + 24X2 = 10 + 5X + -10 + -5X

Combine like terms: -24 + -10 = -34
-34 + -36X + -5X + 24X2 = 10 + 5X + -10 + -5X

Combine like terms: -36X + -5X = -41X
-34 + -41X + 24X2 = 10 + 5X + -10 + -5X

Reorder the terms:
-34 + -41X + 24X2 = 10 + -10 + 5X + -5X

Combine like terms: 10 + -10 = 0
-34 + -41X + 24X2 = 0 + 5X + -5X
-34 + -41X + 24X2 = 5X + -5X

Combine like terms: 5X + -5X = 0
-34 + -41X + 24X2 = 0

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

Divide each side by '24'.
-1.416666667 + -1.708333333X + X2 = 0

Move the constant term to the right:

Add '1.416666667' to each side of the equation.
-1.416666667 + -1.708333333X + 1.416666667 + X2 = 0 + 1.416666667

Reorder the terms:
-1.416666667 + 1.416666667 + -1.708333333X + X2 = 0 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + -1.708333333X + X2 = 0 + 1.416666667
-1.708333333X + X2 = 0 + 1.416666667

Combine like terms: 0 + 1.416666667 = 1.416666667
-1.708333333X + X2 = 1.416666667

The X term is -1.708333333X.  Take half its coefficient (-0.8541666665).
Square it (0.7296006942) and add it to both sides.

Add '0.7296006942' to each side of the equation.
-1.708333333X + 0.7296006942 + X2 = 1.416666667 + 0.7296006942

Reorder the terms:
0.7296006942 + -1.708333333X + X2 = 1.416666667 + 0.7296006942

Combine like terms: 1.416666667 + 0.7296006942 = 2.1462673612
0.7296006942 + -1.708333333X + X2 = 2.1462673612

Factor a perfect square on the left side:
(X + -0.8541666665)(X + -0.8541666665) = 2.1462673612

Calculate the square root of the right side: 1.465014458

Break this problem into two subproblems by setting 
(X + -0.8541666665) equal to 1.465014458 and -1.465014458.

Subproblem 1
X + -0.8541666665 = 1.465014458

Simplifying
X + -0.8541666665 = 1.465014458

Reorder the terms:
-0.8541666665 + X = 1.465014458

Solving
-0.8541666665 + X = 1.465014458

Solving for variable 'X'.

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

Add '0.8541666665' to each side of the equation.
-0.8541666665 + 0.8541666665 + X = 1.465014458 + 0.8541666665

Combine like terms: -0.8541666665 + 0.8541666665 = 0.0000000000
0.0000000000 + X = 1.465014458 + 0.8541666665
X = 1.465014458 + 0.8541666665

Combine like terms: 1.465014458 + 0.8541666665 = 2.3191811245
X = 2.3191811245

Simplifying
X = 2.3191811245

Subproblem 2
X + -0.8541666665 = -1.465014458

Simplifying
X + -0.8541666665 = -1.465014458

Reorder the terms:
-0.8541666665 + X = -1.465014458

Solving
-0.8541666665 + X = -1.465014458

Solving for variable 'X'.

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

Add '0.8541666665' to each side of the equation.
-0.8541666665 + 0.8541666665 + X = -1.465014458 + 0.8541666665

Combine like terms: -0.8541666665 + 0.8541666665 = 0.0000000000
0.0000000000 + X = -1.465014458 + 0.8541666665
X = -1.465014458 + 0.8541666665

Combine like terms: -1.465014458 + 0.8541666665 = -0.6108477915
X = -0.6108477915

Simplifying
X = -0.6108477915

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.3191811245, -0.6108477915}