18a^2-15aq+12aq-10q^2=

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Solution for 18a^2-15aq+12aq-10q^2= equation:


Simplifying
18a2 + -15aq + 12aq + -10q2 = 0

Reorder the terms:
-15aq + 12aq + 18a2 + -10q2 = 0

Combine like terms: -15aq + 12aq = -3aq
-3aq + 18a2 + -10q2 = 0

Solving
-3aq + 18a2 + -10q2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6a + -5q)(3a + 2q) = 0

Subproblem 1

Set the factor '(6a + -5q)' equal to zero and attempt to solve: Simplifying 6a + -5q = 0 Solving 6a + -5q = 0 Move all terms containing a to the left, all other terms to the right. Add '5q' to each side of the equation. 6a + -5q + 5q = 0 + 5q Combine like terms: -5q + 5q = 0 6a + 0 = 0 + 5q 6a = 0 + 5q Remove the zero: 6a = 5q Divide each side by '6'. a = 0.8333333333q Simplifying a = 0.8333333333q

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 = {0.8333333333q, -0.6666666667q}

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