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

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

Simplifying
3(4x + 2) = 5 + x(3 + -1x)

Reorder the terms:
3(2 + 4x) = 5 + x(3 + -1x)
(2 * 3 + 4x * 3) = 5 + x(3 + -1x)
(6 + 12x) = 5 + x(3 + -1x)
6 + 12x = 5 + (3 * x + -1x * x)
6 + 12x = 5 + (3x + -1x2)

Solving
6 + 12x = 5 + 3x + -1x2

Solving for variable 'x'.

Reorder the terms:
6 + -5 + 12x + -3x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Combine like terms: 6 + -5 = 1
1 + 12x + -3x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Combine like terms: 12x + -3x = 9x
1 + 9x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Reorder the terms:
1 + 9x + x2 = 5 + -5 + 3x + -3x + -1x2 + x2

Combine like terms: 5 + -5 = 0
1 + 9x + x2 = 0 + 3x + -3x + -1x2 + x2
1 + 9x + x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
1 + 9x + x2 = 0 + -1x2 + x2
1 + 9x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 9x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 9x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9x + x2 = 0 + -1
9x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
9x + x2 = -1

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -1 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -1 + 20.25

Combine like terms: -1 + 20.25 = 19.25
20.25 + 9x + x2 = 19.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.387482194 and -4.387482194.

Subproblem 1
x + 4.5 = 4.387482194

Simplifying
x + 4.5 = 4.387482194

Reorder the terms:
4.5 + x = 4.387482194

Solving
4.5 + x = 4.387482194

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.387482194 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.387482194 + -4.5
x = 4.387482194 + -4.5

Combine like terms: 4.387482194 + -4.5 = -0.112517806
x = -0.112517806

Simplifying
x = -0.112517806

Subproblem 2
x + 4.5 = -4.387482194

Simplifying
x + 4.5 = -4.387482194

Reorder the terms:
4.5 + x = -4.387482194

Solving
4.5 + x = -4.387482194

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.387482194 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.387482194 + -4.5
x = -4.387482194 + -4.5

Combine like terms: -4.387482194 + -4.5 = -8.887482194
x = -8.887482194

Simplifying
x = -8.887482194

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.112517806, -8.887482194}