3(2z+3)(z-3)=

Solution for 3(2z+3)(z-3)= equation:

Simplifying
3(2z + 3)(z + -3) = 0

Reorder the terms:
3(3 + 2z)(z + -3) = 0

Reorder the terms:
3(3 + 2z)(-3 + z) = 0

Multiply (3 + 2z) * (-3 + z)
3(3(-3 + z) + 2z * (-3 + z)) = 0
3((-3 * 3 + z * 3) + 2z * (-3 + z)) = 0
3((-9 + 3z) + 2z * (-3 + z)) = 0
3(-9 + 3z + (-3 * 2z + z * 2z)) = 0
3(-9 + 3z + (-6z + 2z2)) = 0

Combine like terms: 3z + -6z = -3z
3(-9 + -3z + 2z2) = 0
(-9 * 3 + -3z * 3 + 2z2 * 3) = 0
(-27 + -9z + 6z2) = 0

Solving
-27 + -9z + 6z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -3z + 2z2) = 0

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

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

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

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

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

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {-1.5, 3}