0-(-x^2+4x+3)=(-2x+4)(10-x)

Solution for 0-(-x^2+4x+3)=(-2x+4)(10-x) equation:

Simplifying
0 + -1(-1x2 + 4x + 3) = (-2x + 4)(10 + -1x)

Reorder the terms:
0 + -1(3 + 4x + -1x2) = (-2x + 4)(10 + -1x)
0 + (3 * -1 + 4x * -1 + -1x2 * -1) = (-2x + 4)(10 + -1x)
0 + (-3 + -4x + 1x2) = (-2x + 4)(10 + -1x)

Combine like terms: 0 + -3 = -3
-3 + -4x + 1x2 = (-2x + 4)(10 + -1x)

Reorder the terms:
-3 + -4x + 1x2 = (4 + -2x)(10 + -1x)

Multiply (4 + -2x) * (10 + -1x)
-3 + -4x + 1x2 = (4(10 + -1x) + -2x * (10 + -1x))
-3 + -4x + 1x2 = ((10 * 4 + -1x * 4) + -2x * (10 + -1x))
-3 + -4x + 1x2 = ((40 + -4x) + -2x * (10 + -1x))
-3 + -4x + 1x2 = (40 + -4x + (10 * -2x + -1x * -2x))
-3 + -4x + 1x2 = (40 + -4x + (-20x + 2x2))

Combine like terms: -4x + -20x = -24x
-3 + -4x + 1x2 = (40 + -24x + 2x2)

Solving
-3 + -4x + 1x2 = 40 + -24x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3 + -40 + -4x + 24x + 1x2 + -2x2 = 40 + -24x + 2x2 + -40 + 24x + -2x2

Combine like terms: -3 + -40 = -43
-43 + -4x + 24x + 1x2 + -2x2 = 40 + -24x + 2x2 + -40 + 24x + -2x2

Combine like terms: -4x + 24x = 20x
-43 + 20x + 1x2 + -2x2 = 40 + -24x + 2x2 + -40 + 24x + -2x2

Combine like terms: 1x2 + -2x2 = -1x2
-43 + 20x + -1x2 = 40 + -24x + 2x2 + -40 + 24x + -2x2

Reorder the terms:
-43 + 20x + -1x2 = 40 + -40 + -24x + 24x + 2x2 + -2x2

Combine like terms: 40 + -40 = 0
-43 + 20x + -1x2 = 0 + -24x + 24x + 2x2 + -2x2
-43 + 20x + -1x2 = -24x + 24x + 2x2 + -2x2

Combine like terms: -24x + 24x = 0
-43 + 20x + -1x2 = 0 + 2x2 + -2x2
-43 + 20x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-43 + 20x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
43 + -20x + x2 = 0

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + -20x + -43 + x2 = 0 + -43

Reorder the terms:
43 + -43 + -20x + x2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + -20x + x2 = 0 + -43
-20x + x2 = 0 + -43

Combine like terms: 0 + -43 = -43
-20x + x2 = -43

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -43 + 100

Reorder the terms:
100 + -20x + x2 = -43 + 100

Combine like terms: -43 + 100 = 57
100 + -20x + x2 = 57

Factor a perfect square on the left side:
(x + -10)(x + -10) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + -10) equal to 7.549834435 and -7.549834435.

Subproblem 1
x + -10 = 7.549834435

Simplifying
x + -10 = 7.549834435

Reorder the terms:
-10 + x = 7.549834435

Solving
-10 + x = 7.549834435

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 7.549834435 + 10

Combine like terms: -10 + 10 = 0
0 + x = 7.549834435 + 10
x = 7.549834435 + 10

Combine like terms: 7.549834435 + 10 = 17.549834435
x = 17.549834435

Simplifying
x = 17.549834435

Subproblem 2
x + -10 = -7.549834435

Simplifying
x + -10 = -7.549834435

Reorder the terms:
-10 + x = -7.549834435

Solving
-10 + x = -7.549834435

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -7.549834435 + 10

Combine like terms: -10 + 10 = 0
0 + x = -7.549834435 + 10
x = -7.549834435 + 10

Combine like terms: -7.549834435 + 10 = 2.450165565
x = 2.450165565

Simplifying
x = 2.450165565

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.549834435, 2.450165565}