r^2-17rz+70z^2=0

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Solution for r^2-17rz+70z^2=0 equation:


Simplifying
r2 + -17rz + 70z2 = 0

Reorder the terms:
-17rz + r2 + 70z2 = 0

Solving
-17rz + r2 + 70z2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -10z)(r + -7z) = 0

Subproblem 1

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

Subproblem 2

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

Solution

r = {10z, 7z}

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