z(z-7)=-10

Solution for z(z-7)=-10 equation:

Simplifying
z(z + -7) = -10

Reorder the terms:
z(-7 + z) = -10
(-7 * z + z * z) = -10
(-7z + z2) = -10

Solving
-7z + z2 = -10

Solving for variable 'z'.

Reorder the terms:
10 + -7z + z2 = -10 + 10

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

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

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

Simplifying
5 + -1z = 0

Solving
5 + -1z = 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 + -1z = 0 + -5

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

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

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {2, 5}