3z(2z+7)=12

Solution for 3z(2z+7)=12 equation:

Simplifying
3z(2z + 7) = 12

Reorder the terms:
3z(7 + 2z) = 12
(7 * 3z + 2z * 3z) = 12
(21z + 6z2) = 12

Solving
21z + 6z2 = 12

Solving for variable 'z'.

Reorder the terms:
-12 + 21z + 6z2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 21z + 6z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 7z + 2z2) = 0

Factor a trinomial.
3((-4 + -1z)(1 + -2z)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve:

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4
Subproblem 2
Set the factor '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {-4, 0.5}