0=x+3x^2-4

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

Simplifying
0 = x + 3x2 + -4

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

Solving
0 = -4 + x + 3x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(1 + -1x)(4 + 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 '(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 = {1, -1.333333333}