4(6-x)2(3-x)-5=9(5-2x)

Solution for 4(6-x)2(3-x)-5=9(5-2x) equation:

Simplifying
4(6 + -1x) * 2(3 + -1x) + -5 = 9(5 + -2x)

Reorder the terms for easier multiplication:
4 * 2(6 + -1x)(3 + -1x) + -5 = 9(5 + -2x)

Multiply 4 * 2
8(6 + -1x)(3 + -1x) + -5 = 9(5 + -2x)

Multiply (6 + -1x) * (3 + -1x)
8(6(3 + -1x) + -1x * (3 + -1x)) + -5 = 9(5 + -2x)
8((3 * 6 + -1x * 6) + -1x * (3 + -1x)) + -5 = 9(5 + -2x)
8((18 + -6x) + -1x * (3 + -1x)) + -5 = 9(5 + -2x)
8(18 + -6x + (3 * -1x + -1x * -1x)) + -5 = 9(5 + -2x)
8(18 + -6x + (-3x + 1x2)) + -5 = 9(5 + -2x)

Combine like terms: -6x + -3x = -9x
8(18 + -9x + 1x2) + -5 = 9(5 + -2x)
(18 * 8 + -9x * 8 + 1x2 * 8) + -5 = 9(5 + -2x)
(144 + -72x + 8x2) + -5 = 9(5 + -2x)

Reorder the terms:
144 + -5 + -72x + 8x2 = 9(5 + -2x)

Combine like terms: 144 + -5 = 139
139 + -72x + 8x2 = 9(5 + -2x)
139 + -72x + 8x2 = (5 * 9 + -2x * 9)
139 + -72x + 8x2 = (45 + -18x)

Solving
139 + -72x + 8x2 = 45 + -18x

Solving for variable 'x'.

Reorder the terms:
139 + -45 + -72x + 18x + 8x2 = 45 + -18x + -45 + 18x

Combine like terms: 139 + -45 = 94
94 + -72x + 18x + 8x2 = 45 + -18x + -45 + 18x

Combine like terms: -72x + 18x = -54x
94 + -54x + 8x2 = 45 + -18x + -45 + 18x

Reorder the terms:
94 + -54x + 8x2 = 45 + -45 + -18x + 18x

Combine like terms: 45 + -45 = 0
94 + -54x + 8x2 = 0 + -18x + 18x
94 + -54x + 8x2 = -18x + 18x

Combine like terms: -18x + 18x = 0
94 + -54x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(47 + -27x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(47 + -27x + 4x2)' equal to zero and attempt to solve:

Simplifying
47 + -27x + 4x2 = 0

Solving
47 + -27x + 4x2 = 0

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

Divide each side by '4'.
11.75 + -6.75x + x2 = 0

Move the constant term to the right:

Add '-11.75' to each side of the equation.
11.75 + -6.75x + -11.75 + x2 = 0 + -11.75

Reorder the terms:
11.75 + -11.75 + -6.75x + x2 = 0 + -11.75

Combine like terms: 11.75 + -11.75 = 0.00
0.00 + -6.75x + x2 = 0 + -11.75
-6.75x + x2 = 0 + -11.75

Combine like terms: 0 + -11.75 = -11.75
-6.75x + x2 = -11.75

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = -11.75 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = -11.75 + 11.390625

Combine like terms: -11.75 + 11.390625 = -0.359375
11.390625 + -6.75x + x2 = -0.359375

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = -0.359375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.