(x-5)(x+1)-2x(x-3)=0

Solution for (x-5)(x+1)-2x(x-3)=0 equation:

Simplifying
(x + -5)(x + 1) + -2x(x + -3) = 0

Reorder the terms:
(-5 + x)(x + 1) + -2x(x + -3) = 0

Reorder the terms:
(-5 + x)(1 + x) + -2x(x + -3) = 0

Multiply (-5 + x) * (1 + x)
(-5(1 + x) + x(1 + x)) + -2x(x + -3) = 0
((1 * -5 + x * -5) + x(1 + x)) + -2x(x + -3) = 0
((-5 + -5x) + x(1 + x)) + -2x(x + -3) = 0
(-5 + -5x + (1 * x + x * x)) + -2x(x + -3) = 0
(-5 + -5x + (1x + x2)) + -2x(x + -3) = 0

Combine like terms: -5x + 1x = -4x
(-5 + -4x + x2) + -2x(x + -3) = 0

Reorder the terms:
-5 + -4x + x2 + -2x(-3 + x) = 0
-5 + -4x + x2 + (-3 * -2x + x * -2x) = 0
-5 + -4x + x2 + (6x + -2x2) = 0

Reorder the terms:
-5 + -4x + 6x + x2 + -2x2 = 0

Combine like terms: -4x + 6x = 2x
-5 + 2x + x2 + -2x2 = 0

Combine like terms: x2 + -2x2 = -1x2
-5 + 2x + -1x2 = 0

Solving
-5 + 2x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
5 + -2x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -2x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -2x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x + x2 = 0 + -5
-2x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2x + x2 = -5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -5 + 1

Reorder the terms:
1 + -2x + x2 = -5 + 1

Combine like terms: -5 + 1 = -4
1 + -2x + x2 = -4

Factor a perfect square on the left side:
(x + -1)(x + -1) = -4

Can't calculate square root of the right side.

The solution to this equation could not be determined.