(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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