z(8z+19)=27

Solution for z(8z+19)=27 equation:

Simplifying
z(8z + 19) = 27

Reorder the terms:
z(19 + 8z) = 27
(19 * z + 8z * z) = 27
(19z + 8z2) = 27

Solving
19z + 8z2 = 27

Solving for variable 'z'.

Reorder the terms:
-27 + 19z + 8z2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 19z + 8z2 = 0

Factor a trinomial.
(-27 + -8z)(1 + -1z) = 0

Subproblem 1
Set the factor '(-27 + -8z)' equal to zero and attempt to solve:

Simplifying
-27 + -8z = 0

Solving
-27 + -8z = 0

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

Add '27' to each side of the equation.
-27 + 27 + -8z = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -8z = 0 + 27
-8z = 0 + 27

Combine like terms: 0 + 27 = 27
-8z = 27

Divide each side by '-8'.
z = -3.375

Simplifying
z = -3.375
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

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

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

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

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

Simplifying
z = 1
Solution
z = {-3.375, 1}