4z^2+2(z^2-3)=0

Solution for 4z^2+2(z^2-3)=0 equation:

Simplifying
4z2 + 2(z2 + -3) = 0

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

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

Combine like terms: 4z2 + 2z2 = 6z2
-6 + 6z2 = 0

Solving
-6 + 6z2 = 0

Solving for variable 'z'.

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

Add '6' to each side of the equation.
-6 + 6 + 6z2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 6z2 = 0 + 6
6z2 = 0 + 6

Combine like terms: 0 + 6 = 6
6z2 = 6

Divide each side by '6'.
z2 = 1

Simplifying
z2 = 1

Take the square root of each side:
z = {-1, 1}