2x(x-4)+21(7-x)=45-2x

Solution for 2x(x-4)+21(7-x)=45-2x equation:

Simplifying
2x(x + -4) + 21(7 + -1x) = 45 + -2x

Reorder the terms:
2x(-4 + x) + 21(7 + -1x) = 45 + -2x
(-4 * 2x + x * 2x) + 21(7 + -1x) = 45 + -2x
(-8x + 2x2) + 21(7 + -1x) = 45 + -2x
-8x + 2x2 + (7 * 21 + -1x * 21) = 45 + -2x
-8x + 2x2 + (147 + -21x) = 45 + -2x

Reorder the terms:
147 + -8x + -21x + 2x2 = 45 + -2x

Combine like terms: -8x + -21x = -29x
147 + -29x + 2x2 = 45 + -2x

Solving
147 + -29x + 2x2 = 45 + -2x

Solving for variable 'x'.

Reorder the terms:
147 + -45 + -29x + 2x + 2x2 = 45 + -2x + -45 + 2x

Combine like terms: 147 + -45 = 102
102 + -29x + 2x + 2x2 = 45 + -2x + -45 + 2x

Combine like terms: -29x + 2x = -27x
102 + -27x + 2x2 = 45 + -2x + -45 + 2x

Reorder the terms:
102 + -27x + 2x2 = 45 + -45 + -2x + 2x

Combine like terms: 45 + -45 = 0
102 + -27x + 2x2 = 0 + -2x + 2x
102 + -27x + 2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
102 + -27x + 2x2 = 0

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

Divide each side by '2'.
51 + -13.5x + x2 = 0

Move the constant term to the right:

Add '-51' to each side of the equation.
51 + -13.5x + -51 + x2 = 0 + -51

Reorder the terms:
51 + -51 + -13.5x + x2 = 0 + -51

Combine like terms: 51 + -51 = 0
0 + -13.5x + x2 = 0 + -51
-13.5x + x2 = 0 + -51

Combine like terms: 0 + -51 = -51
-13.5x + x2 = -51

The x term is -13.5x.  Take half its coefficient (-6.75).
Square it (45.5625) and add it to both sides.

Add '45.5625' to each side of the equation.
-13.5x + 45.5625 + x2 = -51 + 45.5625

Reorder the terms:
45.5625 + -13.5x + x2 = -51 + 45.5625

Combine like terms: -51 + 45.5625 = -5.4375
45.5625 + -13.5x + x2 = -5.4375

Factor a perfect square on the left side:
(x + -6.75)(x + -6.75) = -5.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.