28r^4+16r^3-80r^2=0

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Solution for 28r^4+16r^3-80r^2=0 equation:


Simplifying
28r4 + 16r3 + -80r2 = 0

Reorder the terms:
-80r2 + 16r3 + 28r4 = 0

Solving
-80r2 + 16r3 + 28r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4r2'.
4r2(-20 + 4r + 7r2) = 0

Factor a trinomial.
4r2((-2 + -1r)(10 + -7r)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'r2' equal to zero and attempt to solve: Simplifying r2 = 0 Solving r2 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r2 = 0 Take the square root of each side: r = {0}

Subproblem 2

Set the factor '(-2 + -1r)' equal to zero and attempt to solve: Simplifying -2 + -1r = 0 Solving -2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1r = 0 + 2 -1r = 0 + 2 Combine like terms: 0 + 2 = 2 -1r = 2 Divide each side by '-1'. r = -2 Simplifying r = -2

Subproblem 3

Set the factor '(10 + -7r)' equal to zero and attempt to solve: Simplifying 10 + -7r = 0 Solving 10 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -7r = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7r = 0 + -10 -7r = 0 + -10 Combine like terms: 0 + -10 = -10 -7r = -10 Divide each side by '-7'. r = 1.428571429 Simplifying r = 1.428571429

Solution

r = {0, -2, 1.428571429}

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