2(x-4)(x-3)=x-13

Solution for 2(x-4)(x-3)=x-13 equation:

Simplifying
2(x + -4)(x + -3) = x + -13

Reorder the terms:
2(-4 + x)(x + -3) = x + -13

Reorder the terms:
2(-4 + x)(-3 + x) = x + -13

Multiply (-4 + x) * (-3 + x)
2(-4(-3 + x) + x(-3 + x)) = x + -13
2((-3 * -4 + x * -4) + x(-3 + x)) = x + -13
2((12 + -4x) + x(-3 + x)) = x + -13
2(12 + -4x + (-3 * x + x * x)) = x + -13
2(12 + -4x + (-3x + x2)) = x + -13

Combine like terms: -4x + -3x = -7x
2(12 + -7x + x2) = x + -13
(12 * 2 + -7x * 2 + x2 * 2) = x + -13
(24 + -14x + 2x2) = x + -13

Reorder the terms:
24 + -14x + 2x2 = -13 + x

Solving
24 + -14x + 2x2 = -13 + x

Solving for variable 'x'.

Reorder the terms:
24 + 13 + -14x + -1x + 2x2 = -13 + x + 13 + -1x

Combine like terms: 24 + 13 = 37
37 + -14x + -1x + 2x2 = -13 + x + 13 + -1x

Combine like terms: -14x + -1x = -15x
37 + -15x + 2x2 = -13 + x + 13 + -1x

Reorder the terms:
37 + -15x + 2x2 = -13 + 13 + x + -1x

Combine like terms: -13 + 13 = 0
37 + -15x + 2x2 = 0 + x + -1x
37 + -15x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
37 + -15x + 2x2 = 0

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

Divide each side by '2'.
18.5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-18.5' to each side of the equation.
18.5 + -7.5x + -18.5 + x2 = 0 + -18.5

Reorder the terms:
18.5 + -18.5 + -7.5x + x2 = 0 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + -7.5x + x2 = 0 + -18.5
-7.5x + x2 = 0 + -18.5

Combine like terms: 0 + -18.5 = -18.5
-7.5x + x2 = -18.5

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -18.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -18.5 + 14.0625

Combine like terms: -18.5 + 14.0625 = -4.4375
14.0625 + -7.5x + x2 = -4.4375

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = -4.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.