7r^2+3r-4=0

Solution for 7r^2+3r-4=0 equation:

Simplifying
7r2 + 3r + -4 = 0

Reorder the terms:
-4 + 3r + 7r2 = 0

Solving
-4 + 3r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -1r)(4 + -7r) = 0

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

Simplifying
-1 + -1r = 0

Solving
-1 + -1r = 0

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

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

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

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

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

Simplifying
r = -1
Subproblem 2
Set the factor '(4 + -7r)' equal to zero and attempt to solve:

Simplifying
4 + -7r = 0

Solving
4 + -7r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7r = 0 + -4
-7r = 0 + -4

Combine like terms: 0 + -4 = -4
-7r = -4

Divide each side by '-7'.
r = 0.5714285714

Simplifying
r = 0.5714285714
Solution
r = {-1, 0.5714285714}