(r+4)(5r-4)=-16

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Solution for (r+4)(5r-4)=-16 equation: 


Simplifying
(r + 4)(5r + -4) = -16

Reorder the terms:
(4 + r)(5r + -4) = -16

Reorder the terms:
(4 + r)(-4 + 5r) = -16

Multiply (4 + r) * (-4 + 5r)
(4(-4 + 5r) + r(-4 + 5r)) = -16
((-4 * 4 + 5r * 4) + r(-4 + 5r)) = -16
((-16 + 20r) + r(-4 + 5r)) = -16
(-16 + 20r + (-4 * r + 5r * r)) = -16
(-16 + 20r + (-4r + 5r2)) = -16

Combine like terms: 20r + -4r = 16r
(-16 + 16r + 5r2) = -16

Add '16' to each side of the equation.
-16 + 16r + 16 + 5r2 = -16 + 16

Reorder the terms:
-16 + 16 + 16r + 5r2 = -16 + 16

Combine like terms: -16 + 16 = 0
0 + 16r + 5r2 = -16 + 16
16r + 5r2 = -16 + 16

Combine like terms: -16 + 16 = 0
16r + 5r2 = 0

Solving
16r + 5r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(16 + 5r) = 0


Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

Move all terms containing r to the left, all other terms to the right.

Simplifying
r = 0

Subproblem 2
Set the factor '(16 + 5r)' equal to zero and attempt to solve:

Simplifying
16 + 5r = 0

Solving
16 + 5r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -16 + 5r = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 5r = 0 + -16
5r = 0 + -16

Combine like terms: 0 + -16 = -16
5r = -16

Divide each side by '5'.
r = -3.2

Simplifying
r = -3.2
Solution
r = {0, -3.2}

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