(2x-9)(27-4x)=180

Solution for (2x-9)(27-4x)=180 equation:

Simplifying
(2x + -9)(27 + -4x) = 180

Reorder the terms:
(-9 + 2x)(27 + -4x) = 180

Multiply (-9 + 2x) * (27 + -4x)
(-9(27 + -4x) + 2x * (27 + -4x)) = 180
((27 * -9 + -4x * -9) + 2x * (27 + -4x)) = 180
((-243 + 36x) + 2x * (27 + -4x)) = 180
(-243 + 36x + (27 * 2x + -4x * 2x)) = 180
(-243 + 36x + (54x + -8x2)) = 180

Combine like terms: 36x + 54x = 90x
(-243 + 90x + -8x2) = 180

Solving
-243 + 90x + -8x2 = 180

Solving for variable 'x'.

Reorder the terms:
-243 + -180 + 90x + -8x2 = 180 + -180

Combine like terms: -243 + -180 = -423
-423 + 90x + -8x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-423 + 90x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
52.875 + -11.25x + x2 = 0

Move the constant term to the right:

Add '-52.875' to each side of the equation.
52.875 + -11.25x + -52.875 + x2 = 0 + -52.875

Reorder the terms:
52.875 + -52.875 + -11.25x + x2 = 0 + -52.875

Combine like terms: 52.875 + -52.875 = 0.000
0.000 + -11.25x + x2 = 0 + -52.875
-11.25x + x2 = 0 + -52.875

Combine like terms: 0 + -52.875 = -52.875
-11.25x + x2 = -52.875

The x term is -11.25x.  Take half its coefficient (-5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
-11.25x + 31.640625 + x2 = -52.875 + 31.640625

Reorder the terms:
31.640625 + -11.25x + x2 = -52.875 + 31.640625

Combine like terms: -52.875 + 31.640625 = -21.234375
31.640625 + -11.25x + x2 = -21.234375

Factor a perfect square on the left side:
(x + -5.625)(x + -5.625) = -21.234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.