3z^2-14z=5

Solution for 3z^2-14z=5 equation:

Simplifying
3z2 + -14z = 5

Reorder the terms:
-14z + 3z2 = 5

Solving
-14z + 3z2 = 5

Solving for variable 'z'.

Reorder the terms:
-5 + -14z + 3z2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -14z + 3z2 = 0

Factor a trinomial.
(-1 + -3z)(5 + -1z) = 0

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

Simplifying
-1 + -3z = 0

Solving
-1 + -3z = 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 + -3z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3z = 0 + 1
-3z = 0 + 1

Combine like terms: 0 + 1 = 1
-3z = 1

Divide each side by '-3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {-0.3333333333, 5}