z+((z^2)-5)*2=0

Solution for z+((z^2)-5)*2=0 equation:

Simplifying
z + ((z2) + -5) * 2 = 0
z + (z2 + -5) * 2 = 0

Reorder the terms:
z + (-5 + z2) * 2 = 0

Reorder the terms for easier multiplication:
z + 2(-5 + z2) = 0
z + (-5 * 2 + z2 * 2) = 0
z + (-10 + 2z2) = 0

Reorder the terms:
-10 + z + 2z2 = 0

Solving
-10 + z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-5 + -2z)(2 + -1z) = 0

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

Simplifying
-5 + -2z = 0

Solving
-5 + -2z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2z = 0 + 5
-2z = 0 + 5

Combine like terms: 0 + 5 = 5
-2z = 5

Divide each side by '-2'.
z = -2.5

Simplifying
z = -2.5
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-2.5, 2}