4(2r+3)(2r-3)=-2(2r+15)

Solution for 4(2r+3)(2r-3)=-2(2r+15) equation:

Simplifying
4(2r + 3)(2r + -3) = -2(2r + 15)

Reorder the terms:
4(3 + 2r)(2r + -3) = -2(2r + 15)

Reorder the terms:
4(3 + 2r)(-3 + 2r) = -2(2r + 15)

Multiply (3 + 2r) * (-3 + 2r)
4(3(-3 + 2r) + 2r * (-3 + 2r)) = -2(2r + 15)
4((-3 * 3 + 2r * 3) + 2r * (-3 + 2r)) = -2(2r + 15)
4((-9 + 6r) + 2r * (-3 + 2r)) = -2(2r + 15)
4(-9 + 6r + (-3 * 2r + 2r * 2r)) = -2(2r + 15)
4(-9 + 6r + (-6r + 4r2)) = -2(2r + 15)

Combine like terms: 6r + -6r = 0
4(-9 + 0 + 4r2) = -2(2r + 15)
4(-9 + 4r2) = -2(2r + 15)
(-9 * 4 + 4r2 * 4) = -2(2r + 15)
(-36 + 16r2) = -2(2r + 15)

Reorder the terms:
-36 + 16r2 = -2(15 + 2r)
-36 + 16r2 = (15 * -2 + 2r * -2)
-36 + 16r2 = (-30 + -4r)

Solving
-36 + 16r2 = -30 + -4r

Solving for variable 'r'.

Reorder the terms:
-36 + 30 + 4r + 16r2 = -30 + -4r + 30 + 4r

Combine like terms: -36 + 30 = -6
-6 + 4r + 16r2 = -30 + -4r + 30 + 4r

Reorder the terms:
-6 + 4r + 16r2 = -30 + 30 + -4r + 4r

Combine like terms: -30 + 30 = 0
-6 + 4r + 16r2 = 0 + -4r + 4r
-6 + 4r + 16r2 = -4r + 4r

Combine like terms: -4r + 4r = 0
-6 + 4r + 16r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2r + 8r2) = 0

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

Ignore the factor 2.
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 '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

Solving
1 + -2r = 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 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {-0.75, 0.5}