3-4x=-3-x^2+4x

Solution for 3-4x=-3-x^2+4x equation:

Simplifying
3 + -4x = -3 + -1x2 + 4x

Reorder the terms:
3 + -4x = -3 + 4x + -1x2

Solving
3 + -4x = -3 + 4x + -1x2

Solving for variable 'x'.

Reorder the terms:
3 + 3 + -4x + -4x + x2 = -3 + 4x + -1x2 + 3 + -4x + x2

Combine like terms: 3 + 3 = 6
6 + -4x + -4x + x2 = -3 + 4x + -1x2 + 3 + -4x + x2

Combine like terms: -4x + -4x = -8x
6 + -8x + x2 = -3 + 4x + -1x2 + 3 + -4x + x2

Reorder the terms:
6 + -8x + x2 = -3 + 3 + 4x + -4x + -1x2 + x2

Combine like terms: -3 + 3 = 0
6 + -8x + x2 = 0 + 4x + -4x + -1x2 + x2
6 + -8x + x2 = 4x + -4x + -1x2 + x2

Combine like terms: 4x + -4x = 0
6 + -8x + x2 = 0 + -1x2 + x2
6 + -8x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
6 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -8x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -8x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -8x + x2 = 0 + -6
-8x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-8x + x2 = -6

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -6 + 16

Reorder the terms:
16 + -8x + x2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + -8x + x2 = 10

Factor a perfect square on the left side:
(x + -4)(x + -4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -4) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + -4 = 3.16227766

Simplifying
x + -4 = 3.16227766

Reorder the terms:
-4 + x = 3.16227766

Solving
-4 + x = 3.16227766

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.16227766 + 4
x = 3.16227766 + 4

Combine like terms: 3.16227766 + 4 = 7.16227766
x = 7.16227766

Simplifying
x = 7.16227766

Subproblem 2
x + -4 = -3.16227766

Simplifying
x + -4 = -3.16227766

Reorder the terms:
-4 + x = -3.16227766

Solving
-4 + x = -3.16227766

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.16227766 + 4
x = -3.16227766 + 4

Combine like terms: -3.16227766 + 4 = 0.83772234
x = 0.83772234

Simplifying
x = 0.83772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.16227766, 0.83772234}