3z^2-8z-78=6z+2

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Solution for 3z^2-8z-78=6z+2 equation: 


Simplifying
3z2 + -8z + -78 = 6z + 2

Reorder the terms:
-78 + -8z + 3z2 = 6z + 2

Reorder the terms:
-78 + -8z + 3z2 = 2 + 6z

Solving
-78 + -8z + 3z2 = 2 + 6z

Solving for variable 'z'.

Reorder the terms:
-78 + -2 + -8z + -6z + 3z2 = 2 + 6z + -2 + -6z

Combine like terms: -78 + -2 = -80
-80 + -8z + -6z + 3z2 = 2 + 6z + -2 + -6z

Combine like terms: -8z + -6z = -14z
-80 + -14z + 3z2 = 2 + 6z + -2 + -6z

Reorder the terms:
-80 + -14z + 3z2 = 2 + -2 + 6z + -6z

Combine like terms: 2 + -2 = 0
-80 + -14z + 3z2 = 0 + 6z + -6z
-80 + -14z + 3z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
-80 + -14z + 3z2 = 0

Factor a trinomial.
(-10 + -3z)(8 + -1z) = 0


Subproblem 1
Set the factor '(-10 + -3z)' equal to zero and attempt to solve:

Simplifying
-10 + -3z = 0

Solving
-10 + -3z = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3z = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3z = 0 + 10
-3z = 0 + 10

Combine like terms: 0 + 10 = 10
-3z = 10

Divide each side by '-3'.
z = -3.333333333

Simplifying
z = -3.333333333

Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve:

Simplifying
8 + -1z = 0

Solving
8 + -1z = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1z = 0 + -8
-1z = 0 + -8

Combine like terms: 0 + -8 = -8
-1z = -8

Divide each side by '-1'.
z = 8

Simplifying
z = 8
Solution
z = {-3.333333333, 8}

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