8(3x-5)+14-3(3+9x)x=13

Solution for 8(3x-5)+14-3(3+9x)x=13 equation:

Simplifying
8(3x + -5) + 14 + -3(3 + 9x) * x = 13

Reorder the terms:
8(-5 + 3x) + 14 + -3(3 + 9x) * x = 13
(-5 * 8 + 3x * 8) + 14 + -3(3 + 9x) * x = 13
(-40 + 24x) + 14 + -3(3 + 9x) * x = 13

Reorder the terms for easier multiplication:
-40 + 24x + 14 + -3x(3 + 9x) = 13
-40 + 24x + 14 + (3 * -3x + 9x * -3x) = 13
-40 + 24x + 14 + (-9x + -27x2) = 13

Reorder the terms:
-40 + 14 + 24x + -9x + -27x2 = 13

Combine like terms: -40 + 14 = -26
-26 + 24x + -9x + -27x2 = 13

Combine like terms: 24x + -9x = 15x
-26 + 15x + -27x2 = 13

Solving
-26 + 15x + -27x2 = 13

Solving for variable 'x'.

Reorder the terms:
-26 + -13 + 15x + -27x2 = 13 + -13

Combine like terms: -26 + -13 = -39
-39 + 15x + -27x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-39 + 15x + -27x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-13 + 5x + -9x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-13 + 5x + -9x2)' equal to zero and attempt to solve:

Simplifying
-13 + 5x + -9x2 = 0

Solving
-13 + 5x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
1.444444444 + -0.5555555556x + x2 = 0

Move the constant term to the right:

Add '-1.444444444' to each side of the equation.
1.444444444 + -0.5555555556x + -1.444444444 + x2 = 0 + -1.444444444

Reorder the terms:
1.444444444 + -1.444444444 + -0.5555555556x + x2 = 0 + -1.444444444

Combine like terms: 1.444444444 + -1.444444444 = 0.000000000
0.000000000 + -0.5555555556x + x2 = 0 + -1.444444444
-0.5555555556x + x2 = 0 + -1.444444444

Combine like terms: 0 + -1.444444444 = -1.444444444
-0.5555555556x + x2 = -1.444444444

The x term is -0.5555555556x.  Take half its coefficient (-0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
-0.5555555556x + 0.07716049384 + x2 = -1.444444444 + 0.07716049384

Reorder the terms:
0.07716049384 + -0.5555555556x + x2 = -1.444444444 + 0.07716049384

Combine like terms: -1.444444444 + 0.07716049384 = -1.36728395016
0.07716049384 + -0.5555555556x + x2 = -1.36728395016

Factor a perfect square on the left side:
(x + -0.2777777778)(x + -0.2777777778) = -1.36728395016

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.