(r-3)(4r+7)=0

Solution for (r-3)(4r+7)=0 equation:

Simplifying
(r + -3)(4r + 7) = 0

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

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

Multiply (-3 + r) * (7 + 4r)
(-3(7 + 4r) + r(7 + 4r)) = 0
((7 * -3 + 4r * -3) + r(7 + 4r)) = 0
((-21 + -12r) + r(7 + 4r)) = 0
(-21 + -12r + (7 * r + 4r * r)) = 0
(-21 + -12r + (7r + 4r2)) = 0

Combine like terms: -12r + 7r = -5r
(-21 + -5r + 4r2) = 0

Solving
-21 + -5r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7 + -4r)(3 + -1r) = 0

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

Simplifying
-7 + -4r = 0

Solving
-7 + -4r = 0

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

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

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

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

Divide each side by '-4'.
r = -1.75

Simplifying
r = -1.75
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-1.75, 3}