4x(11-3x)=(5x+12)

Solution for 4x(11-3x)=(5x+12) equation:

Simplifying
4x(11 + -3x) = (5x + 12)
(11 * 4x + -3x * 4x) = (5x + 12)
(44x + -12x2) = (5x + 12)

Reorder the terms:
44x + -12x2 = (12 + 5x)

Remove parenthesis around (12 + 5x)
44x + -12x2 = 12 + 5x

Solving
44x + -12x2 = 12 + 5x

Solving for variable 'x'.

Reorder the terms:
-12 + 44x + -5x + -12x2 = 12 + 5x + -12 + -5x

Combine like terms: 44x + -5x = 39x
-12 + 39x + -12x2 = 12 + 5x + -12 + -5x

Reorder the terms:
-12 + 39x + -12x2 = 12 + -12 + 5x + -5x

Combine like terms: 12 + -12 = 0
-12 + 39x + -12x2 = 0 + 5x + -5x
-12 + 39x + -12x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-12 + 39x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 13x + -4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + 13x + -4x2)' equal to zero and attempt to solve:

Simplifying
-4 + 13x + -4x2 = 0

Solving
-4 + 13x + -4x2 = 0

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

Divide each side by '-4'.
1 + -3.25x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.25x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -3.25x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.25x + x2 = 0 + -1
-3.25x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.25x + x2 = -1

The x term is -3.25x.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25x + 2.640625 + x2 = -1 + 2.640625

Reorder the terms:
2.640625 + -3.25x + x2 = -1 + 2.640625

Combine like terms: -1 + 2.640625 = 1.640625
2.640625 + -3.25x + x2 = 1.640625

Factor a perfect square on the left side:
(x + -1.625)(x + -1.625) = 1.640625

Calculate the square root of the right side: 1.280868846

Break this problem into two subproblems by setting 
(x + -1.625) equal to 1.280868846 and -1.280868846.

Subproblem 1
x + -1.625 = 1.280868846

Simplifying
x + -1.625 = 1.280868846

Reorder the terms:
-1.625 + x = 1.280868846

Solving
-1.625 + x = 1.280868846

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = 1.280868846 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = 1.280868846 + 1.625
x = 1.280868846 + 1.625

Combine like terms: 1.280868846 + 1.625 = 2.905868846
x = 2.905868846

Simplifying
x = 2.905868846

Subproblem 2
x + -1.625 = -1.280868846

Simplifying
x + -1.625 = -1.280868846

Reorder the terms:
-1.625 + x = -1.280868846

Solving
-1.625 + x = -1.280868846

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = -1.280868846 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = -1.280868846 + 1.625
x = -1.280868846 + 1.625

Combine like terms: -1.280868846 + 1.625 = 0.344131154
x = 0.344131154

Simplifying
x = 0.344131154

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.905868846, 0.344131154}
Solution
x = {2.905868846, 0.344131154}