(r-4)(r-4)(r-4)=r^3-64

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Solution for (r-4)(r-4)(r-4)=r^3-64 equation: 


Simplifying
(r + -4)(r + -4)(r + -4) = r3 + -64

Reorder the terms:
(-4 + r)(r + -4)(r + -4) = r3 + -64

Reorder the terms:
(-4 + r)(-4 + r)(r + -4) = r3 + -64

Reorder the terms:
(-4 + r)(-4 + r)(-4 + r) = r3 + -64

Multiply (-4 + r) * (-4 + r)
(-4(-4 + r) + r(-4 + r))(-4 + r) = r3 + -64
((-4 * -4 + r * -4) + r(-4 + r))(-4 + r) = r3 + -64
((16 + -4r) + r(-4 + r))(-4 + r) = r3 + -64
(16 + -4r + (-4 * r + r * r))(-4 + r) = r3 + -64
(16 + -4r + (-4r + r2))(-4 + r) = r3 + -64

Combine like terms: -4r + -4r = -8r
(16 + -8r + r2)(-4 + r) = r3 + -64

Multiply (16 + -8r + r2) * (-4 + r)
(16(-4 + r) + -8r * (-4 + r) + r2(-4 + r)) = r3 + -64
((-4 * 16 + r * 16) + -8r * (-4 + r) + r2(-4 + r)) = r3 + -64
((-64 + 16r) + -8r * (-4 + r) + r2(-4 + r)) = r3 + -64
(-64 + 16r + (-4 * -8r + r * -8r) + r2(-4 + r)) = r3 + -64
(-64 + 16r + (32r + -8r2) + r2(-4 + r)) = r3 + -64
(-64 + 16r + 32r + -8r2 + (-4 * r2 + r * r2)) = r3 + -64
(-64 + 16r + 32r + -8r2 + (-4r2 + r3)) = r3 + -64

Combine like terms: 16r + 32r = 48r
(-64 + 48r + -8r2 + -4r2 + r3) = r3 + -64

Combine like terms: -8r2 + -4r2 = -12r2
(-64 + 48r + -12r2 + r3) = r3 + -64

Reorder the terms:
-64 + 48r + -12r2 + r3 = -64 + r3

Add '64' to each side of the equation.
-64 + 48r + -12r2 + 64 + r3 = -64 + 64 + r3

Reorder the terms:
-64 + 64 + 48r + -12r2 + r3 = -64 + 64 + r3

Combine like terms: -64 + 64 = 0
0 + 48r + -12r2 + r3 = -64 + 64 + r3
48r + -12r2 + r3 = -64 + 64 + r3

Combine like terms: -64 + 64 = 0
48r + -12r2 + r3 = 0 + r3
48r + -12r2 + r3 = r3

Add '-1r3' to each side of the equation.
48r + -12r2 + r3 + -1r3 = r3 + -1r3

Combine like terms: r3 + -1r3 = 0
48r + -12r2 + 0 = r3 + -1r3
48r + -12r2 = r3 + -1r3

Combine like terms: r3 + -1r3 = 0
48r + -12r2 = 0

Solving
48r + -12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '12r'.
12r(4 + -1r) = 0

Ignore the factor 12.

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 '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

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

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

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {0, 4}

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