(q+14)(3q-15)=0

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Solution for (q+14)(3q-15)=0 equation:


Simplifying
(q + 14)(3q + -15) = 0

Reorder the terms:
(14 + q)(3q + -15) = 0

Reorder the terms:
(14 + q)(-15 + 3q) = 0

Multiply (14 + q) * (-15 + 3q)
(14(-15 + 3q) + q(-15 + 3q)) = 0
((-15 * 14 + 3q * 14) + q(-15 + 3q)) = 0
((-210 + 42q) + q(-15 + 3q)) = 0
(-210 + 42q + (-15 * q + 3q * q)) = 0
(-210 + 42q + (-15q + 3q2)) = 0

Combine like terms: 42q + -15q = 27q
(-210 + 27q + 3q2) = 0

Solving
-210 + 27q + 3q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-70 + 9q + q2) = 0

Factor a trinomial.
3((-14 + -1q)(5 + -1q)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-14 + -1q)' equal to zero and attempt to solve: Simplifying -14 + -1q = 0 Solving -14 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1q = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1q = 0 + 14 -1q = 0 + 14 Combine like terms: 0 + 14 = 14 -1q = 14 Divide each side by '-1'. q = -14 Simplifying q = -14

Subproblem 2

Set the factor '(5 + -1q)' equal to zero and attempt to solve: Simplifying 5 + -1q = 0 Solving 5 + -1q = 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 + -1q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1q = 0 + -5 -1q = 0 + -5 Combine like terms: 0 + -5 = -5 -1q = -5 Divide each side by '-1'. q = 5 Simplifying q = 5

Solution

q = {-14, 5}

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