(7z^2+4)-(3z^2+2z-6)=

Solution for (7z^2+4)-(3z^2+2z-6)= equation:

Simplifying
(7z2 + 4) + -1(3z2 + 2z + -6) = 0

Reorder the terms:
(4 + 7z2) + -1(3z2 + 2z + -6) = 0

Remove parenthesis around (4 + 7z2)
4 + 7z2 + -1(3z2 + 2z + -6) = 0

Reorder the terms:
4 + 7z2 + -1(-6 + 2z + 3z2) = 0
4 + 7z2 + (-6 * -1 + 2z * -1 + 3z2 * -1) = 0
4 + 7z2 + (6 + -2z + -3z2) = 0

Reorder the terms:
4 + 6 + -2z + 7z2 + -3z2 = 0

Combine like terms: 4 + 6 = 10
10 + -2z + 7z2 + -3z2 = 0

Combine like terms: 7z2 + -3z2 = 4z2
10 + -2z + 4z2 = 0

Solving
10 + -2z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -1z + 2z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1z + 2z2)' equal to zero and attempt to solve:

Simplifying
5 + -1z + 2z2 = 0

Solving
5 + -1z + 2z2 = 0

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

Divide each side by '2'.
2.5 + -0.5z + z2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -0.5z + -2.5 + z2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -0.5z + z2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -0.5z + z2 = 0 + -2.5
-0.5z + z2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-0.5z + z2 = -2.5

The z term is -0.5z.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5z + 0.0625 + z2 = -2.5 + 0.0625

Reorder the terms:
0.0625 + -0.5z + z2 = -2.5 + 0.0625

Combine like terms: -2.5 + 0.0625 = -2.4375
0.0625 + -0.5z + z2 = -2.4375

Factor a perfect square on the left side:
(z + -0.25)(z + -0.25) = -2.4375

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.