(8q+1)(6q-5)=0

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Solution for (8q+1)(6q-5)=0 equation:


Simplifying
(8q + 1)(6q + -5) = 0

Reorder the terms:
(1 + 8q)(6q + -5) = 0

Reorder the terms:
(1 + 8q)(-5 + 6q) = 0

Multiply (1 + 8q) * (-5 + 6q)
(1(-5 + 6q) + 8q * (-5 + 6q)) = 0
((-5 * 1 + 6q * 1) + 8q * (-5 + 6q)) = 0
((-5 + 6q) + 8q * (-5 + 6q)) = 0
(-5 + 6q + (-5 * 8q + 6q * 8q)) = 0
(-5 + 6q + (-40q + 48q2)) = 0

Combine like terms: 6q + -40q = -34q
(-5 + -34q + 48q2) = 0

Solving
-5 + -34q + 48q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-1 + -8q)(5 + -6q) = 0

Subproblem 1

Set the factor '(-1 + -8q)' equal to zero and attempt to solve: Simplifying -1 + -8q = 0 Solving -1 + -8q = 0 Move all terms containing q to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -8q = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8q = 0 + 1 -8q = 0 + 1 Combine like terms: 0 + 1 = 1 -8q = 1 Divide each side by '-8'. q = -0.125 Simplifying q = -0.125

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 = {-0.125, 0.8333333333}

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