7z^2-30z+27=0

Solution for 7z^2-30z+27=0 equation:

Simplifying
7z2 + -30z + 27 = 0

Reorder the terms:
27 + -30z + 7z2 = 0

Solving
27 + -30z + 7z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(9 + -7z)(3 + -1z) = 0

Subproblem 1
Set the factor '(9 + -7z)' equal to zero and attempt to solve:

Simplifying
9 + -7z = 0

Solving
9 + -7z = 0

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

Add '-9' to each side of the equation.
9 + -9 + -7z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7z = 0 + -9
-7z = 0 + -9

Combine like terms: 0 + -9 = -9
-7z = -9

Divide each side by '-7'.
z = 1.285714286

Simplifying
z = 1.285714286
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 = {1.285714286, 3}