0=3x^2-x-4

Solution for 0=3x^2-x-4 equation:

Simplifying
0 = 3x2 + -1x + -4

Reorder the terms:
0 = -4 + -1x + 3x2

Solving
0 = -4 + -1x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 4 = 4
4 + x + -3x2 = -4 + -1x + 3x2 + 4 + x + -3x2

Reorder the terms:
4 + x + -3x2 = -4 + 4 + -1x + x + 3x2 + -3x2

Combine like terms: -4 + 4 = 0
4 + x + -3x2 = 0 + -1x + x + 3x2 + -3x2
4 + x + -3x2 = -1x + x + 3x2 + -3x2

Combine like terms: -1x + x = 0
4 + x + -3x2 = 0 + 3x2 + -3x2
4 + x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
4 + x + -3x2 = 0

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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {1.333333333, -1}