14a^2-33ar+18r^2=0

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Solution for 14a^2-33ar+18r^2=0 equation:


Simplifying
14a2 + -33ar + 18r2 = 0

Reorder the terms:
-33ar + 14a2 + 18r2 = 0

Solving
-33ar + 14a2 + 18r2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -3r)(7a + -6r) = 0

Subproblem 1

Set the factor '(2a + -3r)' equal to zero and attempt to solve: Simplifying 2a + -3r = 0 Solving 2a + -3r = 0 Move all terms containing a to the left, all other terms to the right. Add '3r' to each side of the equation. 2a + -3r + 3r = 0 + 3r Combine like terms: -3r + 3r = 0 2a + 0 = 0 + 3r 2a = 0 + 3r Remove the zero: 2a = 3r Divide each side by '2'. a = 1.5r Simplifying a = 1.5r

Subproblem 2

Set the factor '(7a + -6r)' equal to zero and attempt to solve: Simplifying 7a + -6r = 0 Solving 7a + -6r = 0 Move all terms containing a to the left, all other terms to the right. Add '6r' to each side of the equation. 7a + -6r + 6r = 0 + 6r Combine like terms: -6r + 6r = 0 7a + 0 = 0 + 6r 7a = 0 + 6r Remove the zero: 7a = 6r Divide each side by '7'. a = 0.8571428571r Simplifying a = 0.8571428571r

Solution

a = {1.5r, 0.8571428571r}

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