72q^2-12q-40=0

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Solution for 72q^2-12q-40=0 equation:


Simplifying
72q2 + -12q + -40 = 0

Reorder the terms:
-40 + -12q + 72q2 = 0

Solving
-40 + -12q + 72q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + -3q + 18q2) = 0

Factor a trinomial.
4((-2 + -3q)(5 + -6q)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

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

Solution

q = {-0.6666666667, 0.8333333333}

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