(-5z^2+4z-2)-(2z^2-3z+6)=

Solution for (-5z^2+4z-2)-(2z^2-3z+6)= equation:

Simplifying
(-5z2 + 4z + -2) + -1(2z2 + -3z + 6) = 0

Reorder the terms:
(-2 + 4z + -5z2) + -1(2z2 + -3z + 6) = 0

Remove parenthesis around (-2 + 4z + -5z2)
-2 + 4z + -5z2 + -1(2z2 + -3z + 6) = 0

Reorder the terms:
-2 + 4z + -5z2 + -1(6 + -3z + 2z2) = 0
-2 + 4z + -5z2 + (6 * -1 + -3z * -1 + 2z2 * -1) = 0
-2 + 4z + -5z2 + (-6 + 3z + -2z2) = 0

Reorder the terms:
-2 + -6 + 4z + 3z + -5z2 + -2z2 = 0

Combine like terms: -2 + -6 = -8
-8 + 4z + 3z + -5z2 + -2z2 = 0

Combine like terms: 4z + 3z = 7z
-8 + 7z + -5z2 + -2z2 = 0

Combine like terms: -5z2 + -2z2 = -7z2
-8 + 7z + -7z2 = 0

Solving
-8 + 7z + -7z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
1.142857143 + -1z + z2 = 0

Move the constant term to the right:

Add '-1.142857143' to each side of the equation.
1.142857143 + -1z + -1.142857143 + z2 = 0 + -1.142857143

Reorder the terms:
1.142857143 + -1.142857143 + -1z + z2 = 0 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + -1z + z2 = 0 + -1.142857143
-1z + z2 = 0 + -1.142857143

Combine like terms: 0 + -1.142857143 = -1.142857143
-1z + z2 = -1.142857143

The z term is -1z.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1z + 0.25 + z2 = -1.142857143 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -1.142857143 + 0.25

Combine like terms: -1.142857143 + 0.25 = -0.892857143
0.25 + -1z + z2 = -0.892857143

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = -0.892857143

Can't calculate square root of the right side.

The solution to this equation could not be determined.