5z^2-33z-14=0

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Solution for 5z^2-33z-14=0 equation: 


Simplifying
5z2 + -33z + -14 = 0

Reorder the terms:
-14 + -33z + 5z2 = 0

Solving
-14 + -33z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -5z)(7 + -1z) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1z)' equal to zero and attempt to solve:

Simplifying
7 + -1z = 0

Solving
7 + -1z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1z = 0 + -7
-1z = 0 + -7

Combine like terms: 0 + -7 = -7
-1z = -7

Divide each side by '-1'.
z = 7

Simplifying
z = 7
Solution
z = {-0.4, 7}

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