(-3x^2+3x-7)-(9x^3+5x^2-7)=

Solution for (-3x^2+3x-7)-(9x^3+5x^2-7)= equation:

Simplifying
(-3x2 + 3x + -7) + -1(9x3 + 5x2 + -7) = 0

Reorder the terms:
(-7 + 3x + -3x2) + -1(9x3 + 5x2 + -7) = 0

Remove parenthesis around (-7 + 3x + -3x2)
-7 + 3x + -3x2 + -1(9x3 + 5x2 + -7) = 0

Reorder the terms:
-7 + 3x + -3x2 + -1(-7 + 5x2 + 9x3) = 0
-7 + 3x + -3x2 + (-7 * -1 + 5x2 * -1 + 9x3 * -1) = 0
-7 + 3x + -3x2 + (7 + -5x2 + -9x3) = 0

Reorder the terms:
-7 + 7 + 3x + -3x2 + -5x2 + -9x3 = 0

Combine like terms: -7 + 7 = 0
0 + 3x + -3x2 + -5x2 + -9x3 = 0
3x + -3x2 + -5x2 + -9x3 = 0

Combine like terms: -3x2 + -5x2 = -8x2
3x + -8x2 + -9x3 = 0

Solving
3x + -8x2 + -9x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + -8x + -9x2) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(3 + -8x + -9x2)' equal to zero and attempt to solve:

Simplifying
3 + -8x + -9x2 = 0

Solving
3 + -8x + -9x2 = 0

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

Divide each side by '-9'.
-0.3333333333 + 0.8888888889x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.8888888889x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.8888888889x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.8888888889x + x2 = 0 + 0.3333333333
0.8888888889x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.8888888889x + x2 = 0.3333333333

The x term is 0.8888888889x.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889x + 0.1975308642 + x2 = 0.3333333333 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889x + x2 = 0.3333333333 + 0.1975308642

Combine like terms: 0.3333333333 + 0.1975308642 = 0.5308641975
0.1975308642 + 0.8888888889x + x2 = 0.5308641975

Factor a perfect square on the left side:
(x + 0.4444444445)(x + 0.4444444445) = 0.5308641975

Calculate the square root of the right side: 0.72860428

Break this problem into two subproblems by setting 
(x + 0.4444444445) equal to 0.72860428 and -0.72860428.

Subproblem 1
x + 0.4444444445 = 0.72860428

Simplifying
x + 0.4444444445 = 0.72860428

Reorder the terms:
0.4444444445 + x = 0.72860428

Solving
0.4444444445 + x = 0.72860428

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = 0.72860428 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = 0.72860428 + -0.4444444445
x = 0.72860428 + -0.4444444445

Combine like terms: 0.72860428 + -0.4444444445 = 0.2841598355
x = 0.2841598355

Simplifying
x = 0.2841598355

Subproblem 2
x + 0.4444444445 = -0.72860428

Simplifying
x + 0.4444444445 = -0.72860428

Reorder the terms:
0.4444444445 + x = -0.72860428

Solving
0.4444444445 + x = -0.72860428

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = -0.72860428 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = -0.72860428 + -0.4444444445
x = -0.72860428 + -0.4444444445

Combine like terms: -0.72860428 + -0.4444444445 = -1.1730487245
x = -1.1730487245

Simplifying
x = -1.1730487245

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2841598355, -1.1730487245}
Solution
x = {0, 0.2841598355, -1.1730487245}