0=-3x^2+5x+8

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Solution for 0=-3x^2+5x+8 equation: 


Simplifying
0 = -3x2 + 5x + 8

Reorder the terms:
0 = 8 + 5x + -3x2

Solving
0 = 8 + 5x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + -5x + 3x2 = 8 + 5x + -3x2 + -8 + -5x + 3x2

Reorder the terms:
-8 + -5x + 3x2 = 8 + -8 + 5x + -5x + -3x2 + 3x2

Combine like terms: 8 + -8 = 0
-8 + -5x + 3x2 = 0 + 5x + -5x + -3x2 + 3x2
-8 + -5x + 3x2 = 5x + -5x + -3x2 + 3x2

Combine like terms: 5x + -5x = 0
-8 + -5x + 3x2 = 0 + -3x2 + 3x2
-8 + -5x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-8 + -5x + 3x2 = 0

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


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

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

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

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-1, 2.666666667}

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