(8q-9)(q-3)=0

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Solution for (8q-9)(q-3)=0 equation:


Simplifying
(8q + -9)(q + -3) = 0

Reorder the terms:
(-9 + 8q)(q + -3) = 0

Reorder the terms:
(-9 + 8q)(-3 + q) = 0

Multiply (-9 + 8q) * (-3 + q)
(-9(-3 + q) + 8q * (-3 + q)) = 0
((-3 * -9 + q * -9) + 8q * (-3 + q)) = 0
((27 + -9q) + 8q * (-3 + q)) = 0
(27 + -9q + (-3 * 8q + q * 8q)) = 0
(27 + -9q + (-24q + 8q2)) = 0

Combine like terms: -9q + -24q = -33q
(27 + -33q + 8q2) = 0

Solving
27 + -33q + 8q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(9 + -8q)(3 + -1q) = 0

Subproblem 1

Set the factor '(9 + -8q)' equal to zero and attempt to solve: Simplifying 9 + -8q = 0 Solving 9 + -8q = 0 Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -8q = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8q = 0 + -9 -8q = 0 + -9 Combine like terms: 0 + -9 = -9 -8q = -9 Divide each side by '-8'. q = 1.125 Simplifying q = 1.125

Subproblem 2

Set the factor '(3 + -1q)' equal to zero and attempt to solve: Simplifying 3 + -1q = 0 Solving 3 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1q = 0 + -3 -1q = 0 + -3 Combine like terms: 0 + -3 = -3 -1q = -3 Divide each side by '-1'. q = 3 Simplifying q = 3

Solution

q = {1.125, 3}

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