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

Solution for (r-3)(4r+3)= 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 + -4r)(3 + -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 '(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 = {-0.75, 3}