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

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

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

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

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

Multiply (3 + r) * (-3 + 4r)
(3(-3 + 4r) + r(-3 + 4r)) = 0
((-3 * 3 + 4r * 3) + r(-3 + 4r)) = 0
((-9 + 12r) + r(-3 + 4r)) = 0
(-9 + 12r + (-3 * r + 4r * r)) = 0
(-9 + 12r + (-3r + 4r2)) = 0

Combine like terms: 12r + -3r = 9r
(-9 + 9r + 4r2) = 0

Solving
-9 + 9r + 4r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
Subproblem 2
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
Solution
r = {-3, 0.75}