7z+12z^2-12=0

Solution for 7z+12z^2-12=0 equation:

Simplifying
7z + 12z2 + -12 = 0

Reorder the terms:
-12 + 7z + 12z2 = 0

Solving
-12 + 7z + 12z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-4 + -3z = 0

Solving
-4 + -3z = 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 + -3z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3z = 0 + 4
-3z = 0 + 4

Combine like terms: 0 + 4 = 4
-3z = 4

Divide each side by '-3'.
z = -1.333333333

Simplifying
z = -1.333333333
Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 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 + -4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4z = 0 + -3
-4z = 0 + -3

Combine like terms: 0 + -3 = -3
-4z = -3

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Solution
z = {-1.333333333, 0.75}