2(0.5z^2)=z(z-5)

Solution for 2(0.5z^2)=z(z-5) equation:

Simplifying
2(0.5z2) = z(z + -5)

Remove parenthesis around (0.5z2)
2 * 0.5z2 = z(z + -5)

Multiply 2 * 0.5
1z2 = z(z + -5)

Reorder the terms:
1z2 = z(-5 + z)
1z2 = (-5 * z + z * z)
1z2 = (-5z + z2)

Solving
1z2 = -5z + z2

Solving for variable 'z'.

Reorder the terms:
5z + 1z2 + -1z2 = -5z + z2 + 5z + -1z2

Combine like terms: 1z2 + -1z2 = 0
5z + 0 = -5z + z2 + 5z + -1z2
5z = -5z + z2 + 5z + -1z2

Reorder the terms:
5z = -5z + 5z + z2 + -1z2

Combine like terms: -5z + 5z = 0
5z = 0 + z2 + -1z2
5z = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
5z = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Solution
z = {0}