64a^2-16ab-24b^2=0

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Solution for 64a^2-16ab-24b^2=0 equation:


Simplifying
64a2 + -16ab + -24b2 = 0

Reorder the terms:
-16ab + 64a2 + -24b2 = 0

Solving
-16ab + 64a2 + -24b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-2ab + 8a2 + -3b2) = 0

Factor a trinomial.
8((4a + -3b)(2a + b)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(4a + -3b)' equal to zero and attempt to solve: Simplifying 4a + -3b = 0 Solving 4a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 4a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 4a + 0 = 0 + 3b 4a = 0 + 3b Remove the zero: 4a = 3b Divide each side by '4'. a = 0.75b Simplifying a = 0.75b

Subproblem 2

Set the factor '(2a + b)' equal to zero and attempt to solve: Simplifying 2a + b = 0 Solving 2a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 2a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 2a + 0 = 0 + -1b 2a = 0 + -1b Remove the zero: 2a = -1b Divide each side by '2'. a = -0.5b Simplifying a = -0.5b

Solution

a = {0.75b, -0.5b}

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