0=3x^2-2x-8

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Solution for 0=3x^2-2x-8 equation: 


Simplifying
0 = 3x2 + -2x + -8

Reorder the terms:
0 = -8 + -2x + 3x2

Solving
0 = -8 + -2x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 8 = 8
8 + 2x + -3x2 = -8 + -2x + 3x2 + 8 + 2x + -3x2

Reorder the terms:
8 + 2x + -3x2 = -8 + 8 + -2x + 2x + 3x2 + -3x2

Combine like terms: -8 + 8 = 0
8 + 2x + -3x2 = 0 + -2x + 2x + 3x2 + -3x2
8 + 2x + -3x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
8 + 2x + -3x2 = 0 + 3x2 + -3x2
8 + 2x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
8 + 2x + -3x2 = 0

Factor a trinomial.
(2 + -1x)(4 + 3x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {2, -1.333333333}

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