z(z-9)+9(z-9)=0

Solution for z(z-9)+9(z-9)=0 equation:

Simplifying
z(z + -9) + 9(z + -9) = 0

Reorder the terms:
z(-9 + z) + 9(z + -9) = 0
(-9 * z + z * z) + 9(z + -9) = 0
(-9z + z2) + 9(z + -9) = 0

Reorder the terms:
-9z + z2 + 9(-9 + z) = 0
-9z + z2 + (-9 * 9 + z * 9) = 0
-9z + z2 + (-81 + 9z) = 0

Reorder the terms:
-81 + -9z + 9z + z2 = 0

Combine like terms: -9z + 9z = 0
-81 + 0 + z2 = 0
-81 + z2 = 0

Solving
-81 + z2 = 0

Solving for variable 'z'.

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

Add '81' to each side of the equation.
-81 + 81 + z2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + z2 = 0 + 81
z2 = 0 + 81

Combine like terms: 0 + 81 = 81
z2 = 81

Simplifying
z2 = 81

Take the square root of each side:
z = {-9, 9}