(4r+3)(4r+12)=

Solution for (4r+3)(4r+12)= equation:

Simplifying
(4r + 3)(4r + 12) = 0

Reorder the terms:
(3 + 4r)(4r + 12) = 0

Reorder the terms:
(3 + 4r)(12 + 4r) = 0

Multiply (3 + 4r) * (12 + 4r)
(3(12 + 4r) + 4r * (12 + 4r)) = 0
((12 * 3 + 4r * 3) + 4r * (12 + 4r)) = 0
((36 + 12r) + 4r * (12 + 4r)) = 0
(36 + 12r + (12 * 4r + 4r * 4r)) = 0
(36 + 12r + (48r + 16r2)) = 0

Combine like terms: 12r + 48r = 60r
(36 + 60r + 16r2) = 0

Solving
36 + 60r + 16r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + 15r + 4r2) = 0

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

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

Simplifying
3 + r = 0

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

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

Combine like terms: 0 + -3 = -3
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}