(4r+1)(3r-3)=

Solution for (4r+1)(3r-3)= equation:

Simplifying
(4r + 1)(3r + -3) = 0

Reorder the terms:
(1 + 4r)(3r + -3) = 0

Reorder the terms:
(1 + 4r)(-3 + 3r) = 0

Multiply (1 + 4r) * (-3 + 3r)
(1(-3 + 3r) + 4r * (-3 + 3r)) = 0
((-3 * 1 + 3r * 1) + 4r * (-3 + 3r)) = 0
((-3 + 3r) + 4r * (-3 + 3r)) = 0
(-3 + 3r + (-3 * 4r + 3r * 4r)) = 0
(-3 + 3r + (-12r + 12r2)) = 0

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

Solving
-3 + -9r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -3r + 4r2) = 0

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

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

Simplifying
-1 + -4r = 0

Solving
-1 + -4r = 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 + -4r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4r = 0 + 1
-4r = 0 + 1

Combine like terms: 0 + 1 = 1
-4r = 1

Divide each side by '-4'.
r = -0.25

Simplifying
r = -0.25
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 = {-0.25, 1}