(z+12)(6z-9)=0

Solution for (z+12)(6z-9)=0 equation:

Simplifying
(z + 12)(6z + -9) = 0

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

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

Multiply (12 + z) * (-9 + 6z)
(12(-9 + 6z) + z(-9 + 6z)) = 0
((-9 * 12 + 6z * 12) + z(-9 + 6z)) = 0
((-108 + 72z) + z(-9 + 6z)) = 0
(-108 + 72z + (-9 * z + 6z * z)) = 0
(-108 + 72z + (-9z + 6z2)) = 0

Combine like terms: 72z + -9z = 63z
(-108 + 63z + 6z2) = 0

Solving
-108 + 63z + 6z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-36 + 21z + 2z2) = 0

Factor a trinomial.
3((-12 + -1z)(3 + -2z)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-12 + -1z)' equal to zero and attempt to solve:

Simplifying
-12 + -1z = 0

Solving
-12 + -1z = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1z = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1z = 0 + 12
-1z = 0 + 12

Combine like terms: 0 + 12 = 12
-1z = 12

Divide each side by '-1'.
z = -12

Simplifying
z = -12
Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

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

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {-12, 1.5}