30=z(z-7)

Solution for 30=z(z-7) equation:

Simplifying
30 = z(z + -7)

Reorder the terms:
30 = z(-7 + z)
30 = (-7 * z + z * z)
30 = (-7z + z2)

Solving
30 = -7z + z2

Solving for variable 'z'.

Reorder the terms:
30 + 7z + -1z2 = -7z + 7z + z2 + -1z2

Combine like terms: -7z + 7z = 0
30 + 7z + -1z2 = 0 + z2 + -1z2
30 + 7z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
30 + 7z + -1z2 = 0

Factor a trinomial.
(10 + -1z)(3 + z) = 0

Subproblem 1
Set the factor '(10 + -1z)' equal to zero and attempt to solve:

Simplifying
10 + -1z = 0

Solving
10 + -1z = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1z = 0 + -10
-1z = 0 + -10

Combine like terms: 0 + -10 = -10
-1z = -10

Divide each side by '-1'.
z = 10

Simplifying
z = 10
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Solution
z = {10, -3}