2r^2(r-4)=42r

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Solution for 2r^2(r-4)=42r equation: 


Simplifying
2r2(r + -4) = 42r

Reorder the terms:
2r2(-4 + r) = 42r
(-4 * 2r2 + r * 2r2) = 42r
(-8r2 + 2r3) = 42r

Solving
-8r2 + 2r3 = 42r

Solving for variable 'r'.

Reorder the terms:
-42r + -8r2 + 2r3 = 42r + -42r

Combine like terms: 42r + -42r = 0
-42r + -8r2 + 2r3 = 0

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-21 + -4r + r2) = 0

Factor a trinomial.
2r((-3 + -1r)(7 + -1r)) = 0

Ignore the factor 2.

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 '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 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 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3

Subproblem 3
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {0, -3, 7}

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