(4r+1)(2r-3)=

Solution for (4r+1)(2r-3)= equation:

Simplifying
(4r + 1)(2r + -3) = 0

Reorder the terms:
(1 + 4r)(2r + -3) = 0

Reorder the terms:
(1 + 4r)(-3 + 2r) = 0

Multiply (1 + 4r) * (-3 + 2r)
(1(-3 + 2r) + 4r * (-3 + 2r)) = 0
((-3 * 1 + 2r * 1) + 4r * (-3 + 2r)) = 0
((-3 + 2r) + 4r * (-3 + 2r)) = 0
(-3 + 2r + (-3 * 4r + 2r * 4r)) = 0
(-3 + 2r + (-12r + 8r2)) = 0

Combine like terms: 2r + -12r = -10r
(-3 + -10r + 8r2) = 0

Solving
-3 + -10r + 8r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -4r)(3 + -2r) = 0

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 '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {-0.25, 1.5}