What is 2q^3+24q^2<=-32q ?

The solution to 2q^3+24q^2<=-32q is q<=-2(3+sqrt(5))\lor 2(sqrt(5)-3)<= q<= 0

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2q^3+24q^2<=-32q

2 q^{3} + 24 q^{2} \leq - 32 q

q \leq - 2 (3 + 5) or 2 (5 - 3) \leq q \leq 0

Interval Notation

(- \infty, - 2 (3 + 5)] \cup [2 (5 - 3), 0]

Decimal Notation

q \leq - 10.47213 \dots or - 1.52786 \dots \leq q \leq 0

Solution steps

2 q^{3} + 24 q^{2} \leq - 32 q

Rewrite in standard form

q^{3} + 12 q^{2} + 16 q \leq 0

Factor

q^{3} + 12 q^{2} + 16 q : q (q - 2 (5 - 3)) (q + 2 (3 + 5))

q (q - 2 (5 - 3)) (q + 2 (3 + 5)) \leq 0

Identify the intervals

q \leq - 2 (3 + 5) or 2 (5 - 3) \leq q \leq 0

\frac{3 + 5 i}{4 - 9 i}

125 b^{2} - 180

- \frac{1 ^{2}}{2}

5 (2 - w) - w = 2 (w + 1)

lo g_{\frac{1}{3}} (9)

What is 2q^3+24q^2<=-32q ?
The solution to 2q^3+24q^2<=-32q is q<=-2(3+sqrt(5))\lor 2(sqrt(5)-3)<= q<= 0