24a^2-9aq+16aq-6q^2=

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Solution for 24a^2-9aq+16aq-6q^2= equation:


Simplifying
24a2 + -9aq + 16aq + -6q2 = 0

Reorder the terms:
-9aq + 16aq + 24a2 + -6q2 = 0

Combine like terms: -9aq + 16aq = 7aq
7aq + 24a2 + -6q2 = 0

Solving
7aq + 24a2 + -6q2 = 0

Solving for variable 'a'.

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

Subproblem 1

Set the factor '(8a + -3q)' equal to zero and attempt to solve: Simplifying 8a + -3q = 0 Solving 8a + -3q = 0 Move all terms containing a to the left, all other terms to the right. Add '3q' to each side of the equation. 8a + -3q + 3q = 0 + 3q Combine like terms: -3q + 3q = 0 8a + 0 = 0 + 3q 8a = 0 + 3q Remove the zero: 8a = 3q Divide each side by '8'. a = 0.375q Simplifying a = 0.375q

Subproblem 2

Set the factor '(3a + 2q)' equal to zero and attempt to solve: Simplifying 3a + 2q = 0 Solving 3a + 2q = 0 Move all terms containing a to the left, all other terms to the right. Add '-2q' to each side of the equation. 3a + 2q + -2q = 0 + -2q Combine like terms: 2q + -2q = 0 3a + 0 = 0 + -2q 3a = 0 + -2q Remove the zero: 3a = -2q Divide each side by '3'. a = -0.6666666667q Simplifying a = -0.6666666667q

Solution

a = {0.375q, -0.6666666667q}

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