(z-6)(2z+9)=0

Solution for (z-6)(2z+9)=0 equation:

Simplifying
(z + -6)(2z + 9) = 0

Reorder the terms:
(-6 + z)(2z + 9) = 0

Reorder the terms:
(-6 + z)(9 + 2z) = 0

Multiply (-6 + z) * (9 + 2z)
(-6(9 + 2z) + z(9 + 2z)) = 0
((9 * -6 + 2z * -6) + z(9 + 2z)) = 0
((-54 + -12z) + z(9 + 2z)) = 0
(-54 + -12z + (9 * z + 2z * z)) = 0
(-54 + -12z + (9z + 2z2)) = 0

Combine like terms: -12z + 9z = -3z
(-54 + -3z + 2z2) = 0

Solving
-54 + -3z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + -2z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-9 + -2z)' equal to zero and attempt to solve:

Simplifying
-9 + -2z = 0

Solving
-9 + -2z = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2z = 0 + 9
-2z = 0 + 9

Combine like terms: 0 + 9 = 9
-2z = 9

Divide each side by '-2'.
z = -4.5

Simplifying
z = -4.5
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-4.5, 6}