30z^2+42z+12=0

Solution for 30z^2+42z+12=0 equation:

Simplifying
30z2 + 42z + 12 = 0

Reorder the terms:
12 + 42z + 30z2 = 0

Solving
12 + 42z + 30z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + 7z + 5z2) = 0

Factor a trinomial.
6((1 + z)(2 + 5z)) = 0

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

Simplifying
1 + z = 0

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

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

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

Simplifying
z = -1
Subproblem 2
Set the factor '(2 + 5z)' equal to zero and attempt to solve:

Simplifying
2 + 5z = 0

Solving
2 + 5z = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5z = 0 + -2
5z = 0 + -2

Combine like terms: 0 + -2 = -2
5z = -2

Divide each side by '5'.
z = -0.4

Simplifying
z = -0.4
Solution
z = {-1, -0.4}