0=6x^2-5x-34

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Solution for 0=6x^2-5x-34 equation:


Simplifying
0 = 6x2 + -5x + -34

Reorder the terms:
0 = -34 + -5x + 6x2

Solving
0 = -34 + -5x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 34 = 34
34 + 5x + -6x2 = -34 + -5x + 6x2 + 34 + 5x + -6x2

Reorder the terms:
34 + 5x + -6x2 = -34 + 34 + -5x + 5x + 6x2 + -6x2

Combine like terms: -34 + 34 = 0
34 + 5x + -6x2 = 0 + -5x + 5x + 6x2 + -6x2
34 + 5x + -6x2 = -5x + 5x + 6x2 + -6x2

Combine like terms: -5x + 5x = 0
34 + 5x + -6x2 = 0 + 6x2 + -6x2
34 + 5x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
34 + 5x + -6x2 = 0

Factor a trinomial.
(17 + -6x)(2 + x) = 0


Subproblem 1
Set the factor '(17 + -6x)' equal to zero and attempt to solve:

Simplifying
17 + -6x = 0

Solving
17 + -6x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -6x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -6x = 0 + -17
-6x = 0 + -17

Combine like terms: 0 + -17 = -17
-6x = -17

Divide each side by '-6'.
x = 2.833333333

Simplifying
x = 2.833333333

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {2.833333333, -2}

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