0=4x^2+x-3

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

Simplifying
0 = 4x2 + x + -3

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

Solving
0 = -3 + x + 4x2

Solving for variable 'x'.

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

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

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

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

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

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

Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

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

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
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 = {0.75, -1}