(18z-6)(12z+14)=0

Solution for (18z-6)(12z+14)=0 equation:

Simplifying
(18z + -6)(12z + 14) = 0

Reorder the terms:
(-6 + 18z)(12z + 14) = 0

Reorder the terms:
(-6 + 18z)(14 + 12z) = 0

Multiply (-6 + 18z) * (14 + 12z)
(-6(14 + 12z) + 18z * (14 + 12z)) = 0
((14 * -6 + 12z * -6) + 18z * (14 + 12z)) = 0
((-84 + -72z) + 18z * (14 + 12z)) = 0
(-84 + -72z + (14 * 18z + 12z * 18z)) = 0
(-84 + -72z + (252z + 216z2)) = 0

Combine like terms: -72z + 252z = 180z
(-84 + 180z + 216z2) = 0

Solving
-84 + 180z + 216z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-7 + 15z + 18z2) = 0

Factor a trinomial.
12((-7 + -6z)(1 + -3z)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-7 + -6z)' equal to zero and attempt to solve:

Simplifying
-7 + -6z = 0

Solving
-7 + -6z = 0

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

Add '7' to each side of the equation.
-7 + 7 + -6z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6z = 0 + 7
-6z = 0 + 7

Combine like terms: 0 + 7 = 7
-6z = 7

Divide each side by '-6'.
z = -1.166666667

Simplifying
z = -1.166666667
Subproblem 2
Set the factor '(1 + -3z)' equal to zero and attempt to solve:

Simplifying
1 + -3z = 0

Solving
1 + -3z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3z = 0 + -1
-3z = 0 + -1

Combine like terms: 0 + -1 = -1
-3z = -1

Divide each side by '-3'.
z = 0.3333333333

Simplifying
z = 0.3333333333
Solution
z = {-1.166666667, 0.3333333333}