(x-4)(9-x)+(x+6)=5x

Solution for (x-4)(9-x)+(x+6)=5x equation:

Simplifying
(x + -4)(9 + -1x) + (x + 6) = 5x

Reorder the terms:
(-4 + x)(9 + -1x) + (x + 6) = 5x

Multiply (-4 + x) * (9 + -1x)
(-4(9 + -1x) + x(9 + -1x)) + (x + 6) = 5x
((9 * -4 + -1x * -4) + x(9 + -1x)) + (x + 6) = 5x
((-36 + 4x) + x(9 + -1x)) + (x + 6) = 5x
(-36 + 4x + (9 * x + -1x * x)) + (x + 6) = 5x
(-36 + 4x + (9x + -1x2)) + (x + 6) = 5x

Combine like terms: 4x + 9x = 13x
(-36 + 13x + -1x2) + (x + 6) = 5x

Reorder the terms:
-36 + 13x + -1x2 + (6 + x) = 5x

Remove parenthesis around (6 + x)
-36 + 13x + -1x2 + 6 + x = 5x

Reorder the terms:
-36 + 6 + 13x + x + -1x2 = 5x

Combine like terms: -36 + 6 = -30
-30 + 13x + x + -1x2 = 5x

Combine like terms: 13x + x = 14x
-30 + 14x + -1x2 = 5x

Solving
-30 + 14x + -1x2 = 5x

Solving for variable 'x'.

Reorder the terms:
-30 + 14x + -5x + -1x2 = 5x + -5x

Combine like terms: 14x + -5x = 9x
-30 + 9x + -1x2 = 5x + -5x

Combine like terms: 5x + -5x = 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.