4r^2-7r=-3

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

Simplifying
4r2 + -7r = -3

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

Solving
-7r + 4r2 = -3

Solving for variable 'r'.

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

Combine like terms: -3 + 3 = 0
3 + -7r + 4r2 = 0

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

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

Simplifying
3 + -4r = 0

Solving
3 + -4r = 0

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

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

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

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

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

Simplifying
r = 0.75
Subproblem 2
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
Solution
r = {0.75, 1}