(-7z^2+6z-1)-(2z^2+5z-4)=

Solution for (-7z^2+6z-1)-(2z^2+5z-4)= equation:

Simplifying
(-7z2 + 6z + -1) + -1(2z2 + 5z + -4) = 0

Reorder the terms:
(-1 + 6z + -7z2) + -1(2z2 + 5z + -4) = 0

Remove parenthesis around (-1 + 6z + -7z2)
-1 + 6z + -7z2 + -1(2z2 + 5z + -4) = 0

Reorder the terms:
-1 + 6z + -7z2 + -1(-4 + 5z + 2z2) = 0
-1 + 6z + -7z2 + (-4 * -1 + 5z * -1 + 2z2 * -1) = 0
-1 + 6z + -7z2 + (4 + -5z + -2z2) = 0

Reorder the terms:
-1 + 4 + 6z + -5z + -7z2 + -2z2 = 0

Combine like terms: -1 + 4 = 3
3 + 6z + -5z + -7z2 + -2z2 = 0

Combine like terms: 6z + -5z = 1z
3 + 1z + -7z2 + -2z2 = 0

Combine like terms: -7z2 + -2z2 = -9z2
3 + 1z + -9z2 = 0

Solving
3 + 1z + -9z2 = 0

Solving for variable 'z'.

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

Divide each side by '-9'.
-0.3333333333 + -0.1111111111z + z2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -0.1111111111z + 0.3333333333 + z2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -0.1111111111z + z2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -0.1111111111z + z2 = 0 + 0.3333333333
-0.1111111111z + z2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-0.1111111111z + z2 = 0.3333333333

The z term is -0.1111111111z.  Take half its coefficient (-0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
-0.1111111111z + 0.003086419752 + z2 = 0.3333333333 + 0.003086419752

Reorder the terms:
0.003086419752 + -0.1111111111z + z2 = 0.3333333333 + 0.003086419752

Combine like terms: 0.3333333333 + 0.003086419752 = 0.336419753052
0.003086419752 + -0.1111111111z + z2 = 0.336419753052

Factor a perfect square on the left side:
(z + -0.05555555555)(z + -0.05555555555) = 0.336419753052

Calculate the square root of the right side: 0.580017028

Break this problem into two subproblems by setting 
(z + -0.05555555555) equal to 0.580017028 and -0.580017028.

Subproblem 1
z + -0.05555555555 = 0.580017028

Simplifying
z + -0.05555555555 = 0.580017028

Reorder the terms:
-0.05555555555 + z = 0.580017028

Solving
-0.05555555555 + z = 0.580017028

Solving for variable 'z'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + z = 0.580017028 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + z = 0.580017028 + 0.05555555555
z = 0.580017028 + 0.05555555555

Combine like terms: 0.580017028 + 0.05555555555 = 0.63557258355
z = 0.63557258355

Simplifying
z = 0.63557258355

Subproblem 2
z + -0.05555555555 = -0.580017028

Simplifying
z + -0.05555555555 = -0.580017028

Reorder the terms:
-0.05555555555 + z = -0.580017028

Solving
-0.05555555555 + z = -0.580017028

Solving for variable 'z'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + z = -0.580017028 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + z = -0.580017028 + 0.05555555555
z = -0.580017028 + 0.05555555555

Combine like terms: -0.580017028 + 0.05555555555 = -0.52446147245
z = -0.52446147245

Simplifying
z = -0.52446147245

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.63557258355, -0.52446147245}