(x-4)(-x+5)=10

Solution for (x-4)(-x+5)=10 equation:

Simplifying
(x + -4)(-1x + 5) = 10

Reorder the terms:
(-4 + x)(-1x + 5) = 10

Reorder the terms:
(-4 + x)(5 + -1x) = 10

Multiply (-4 + x) * (5 + -1x)
(-4(5 + -1x) + x(5 + -1x)) = 10
((5 * -4 + -1x * -4) + x(5 + -1x)) = 10
((-20 + 4x) + x(5 + -1x)) = 10
(-20 + 4x + (5 * x + -1x * x)) = 10
(-20 + 4x + (5x + -1x2)) = 10

Combine like terms: 4x + 5x = 9x
(-20 + 9x + -1x2) = 10

Solving
-20 + 9x + -1x2 = 10

Solving for variable 'x'.

Reorder the terms:
-20 + -10 + 9x + -1x2 = 10 + -10

Combine like terms: -20 + -10 = -30
-30 + 9x + -1x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-30 + 9x + -1x2 = 0

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

Divide each side by '-1'.
30 + -9x + x2 = 0

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -9x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + -9x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -9x + x2 = 0 + -30
-9x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
-9x + x2 = -30

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 = -30 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -30 + 20.25

Combine like terms: -30 + 20.25 = -9.75
20.25 + -9x + x2 = -9.75

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = -9.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.