-7q^2+105q-378=0

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Solution for -7q^2+105q-378=0 equation:


Simplifying
-7q2 + 105q + -378 = 0

Reorder the terms:
-378 + 105q + -7q2 = 0

Solving
-378 + 105q + -7q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-54 + 15q + -1q2) = 0

Factor a trinomial.
7((-9 + q)(6 + -1q)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-9 + q)' equal to zero and attempt to solve: Simplifying -9 + q = 0 Solving -9 + q = 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 + q = 0 + 9 Combine like terms: -9 + 9 = 0 0 + q = 0 + 9 q = 0 + 9 Combine like terms: 0 + 9 = 9 q = 9 Simplifying q = 9

Subproblem 2

Set the factor '(6 + -1q)' equal to zero and attempt to solve: Simplifying 6 + -1q = 0 Solving 6 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1q = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1q = 0 + -6 -1q = 0 + -6 Combine like terms: 0 + -6 = -6 -1q = -6 Divide each side by '-1'. q = 6 Simplifying q = 6

Solution

q = {9, 6}

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