0=4x^2+x-5

Solution for 0=4x^2+x-5 equation:

Simplifying
0 = 4x2 + x + -5

Reorder the terms:
0 = -5 + x + 4x2

Solving
0 = -5 + x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 5 = 5
5 + -1x + -4x2 = -5 + x + 4x2 + 5 + -1x + -4x2

Reorder the terms:
5 + -1x + -4x2 = -5 + 5 + x + -1x + 4x2 + -4x2

Combine like terms: -5 + 5 = 0
5 + -1x + -4x2 = 0 + x + -1x + 4x2 + -4x2
5 + -1x + -4x2 = x + -1x + 4x2 + -4x2

Combine like terms: x + -1x = 0
5 + -1x + -4x2 = 0 + 4x2 + -4x2
5 + -1x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
5 + -1x + -4x2 = 0

Factor a trinomial.
(1 + -1x)(5 + 4x) = 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 '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {1, -1.25}