27ay-14y^2=10a^2

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Solution for 27ay-14y^2=10a^2 equation:


Simplifying
27ay + -14y2 = 10a2

Solving
27ay + -14y2 = 10a2

Solving for variable 'a'.

Reorder the terms:
27ay + -10a2 + -14y2 = 10a2 + -10a2

Combine like terms: 10a2 + -10a2 = 0
27ay + -10a2 + -14y2 = 0

Factor a trinomial.
(-10a + 7y)(a + -2y) = 0

Subproblem 1

Set the factor '(-10a + 7y)' equal to zero and attempt to solve: Simplifying -10a + 7y = 0 Solving -10a + 7y = 0 Move all terms containing a to the left, all other terms to the right. Add '-7y' to each side of the equation. -10a + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 -10a + 0 = 0 + -7y -10a = 0 + -7y Remove the zero: -10a = -7y Divide each side by '-10'. a = 0.7y Simplifying a = 0.7y

Subproblem 2

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

Solution

a = {0.7y, 2y}

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