2r^2+10rs-28s^2=0

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Solution for 2r^2+10rs-28s^2=0 equation:


Simplifying
2r2 + 10rs + -28s2 = 0

Reorder the terms:
10rs + 2r2 + -28s2 = 0

Solving
10rs + 2r2 + -28s2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5rs + r2 + -14s2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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

Solution

r = {2s, -7s}

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