-24q^2-90q=21

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Solution for -24q^2-90q=21 equation:


Simplifying
-24q2 + -90q = 21

Reorder the terms:
-90q + -24q2 = 21

Solving
-90q + -24q2 = 21

Solving for variable 'q'.

Reorder the terms:
-21 + -90q + -24q2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -90q + -24q2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(7 + 30q + 8q2) = 0

Factor a trinomial.
-3((7 + 2q)(1 + 4q)) = 0

Ignore the factor -3.

Subproblem 1

Set the factor '(7 + 2q)' equal to zero and attempt to solve: Simplifying 7 + 2q = 0 Solving 7 + 2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2q = 0 + -7 2q = 0 + -7 Combine like terms: 0 + -7 = -7 2q = -7 Divide each side by '2'. q = -3.5 Simplifying q = -3.5

Subproblem 2

Set the factor '(1 + 4q)' equal to zero and attempt to solve: Simplifying 1 + 4q = 0 Solving 1 + 4q = 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 + 4q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4q = 0 + -1 4q = 0 + -1 Combine like terms: 0 + -1 = -1 4q = -1 Divide each side by '4'. q = -0.25 Simplifying q = -0.25

Solution

q = {-3.5, -0.25}

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