Solve (12s^(4)-6s^(2) 4s) (6s^(4)-4s^27)-(4s^(4) s^(2 - ScanMath

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Type your math problem... (12s^(4)-6s^(2) 4s) (6s^(4)-4s^27)-(4s^(4) s^(2) 12)

Question

Simplify the expression

72 s^{8} - 384 s^{6} - 144 s^{7} + 672 s^{5}

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Factor the expression

24 s^{5} (3 s^{3} - 16 s - 6 s^{2} + 28)

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Find the roots

s_{1} \approx - 2.240288, s_{2} = 0, s_{3} \approx 1.546664, s_{4} \approx 2.693623

Evaluate

(12 s^{4} - 6 s^{2} \times 4 s) (6 s^{4} - 4 s^{2} \times 7) - (4 s^{4} \times s^{2} \times 12)

To find the roots of the expression,set the expression equal to 0

(12 s^{4} - 6 s^{2} \times 4 s) (6 s^{4} - 4 s^{2} \times 7) - (4 s^{4} \times s^{2} \times 12) = 0

Multiply

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(12 s^{4} - 24 s^{3}) (6 s^{4} - 4 s^{2} \times 7) - (4 s^{4} \times s^{2} \times 12) = 0

Multiply the terms

(12 s^{4} - 24 s^{3}) (6 s^{4} - 28 s^{2}) - (4 s^{4} \times s^{2} \times 12) = 0

Multiply

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(12 s^{4} - 24 s^{3}) (6 s^{4} - 28 s^{2}) - 48 s^{6} = 0

Calculate

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72 s^{8} - 384 s^{6} - 144 s^{7} + 672 s^{5} = 0

Factor the expression

24 s^{5} (3 s^{3} - 16 s - 6 s^{2} + 28) = 0

Divide both sides

s^{5} (3 s^{3} - 16 s - 6 s^{2} + 28) = 0

Separate the equation into 2 possible cases

s^{5} = 0 3 s^{3} - 16 s - 6 s^{2} + 28 = 0

The only way a power can be 0 is when the base equals 0

s = 0 3 s^{3} - 16 s - 6 s^{2} + 28 = 0

Solve the equation

s = 0 s \approx - 2.240288 s \approx 1.546664 s \approx 2.693623

Solution

s_{1} \approx - 2.240288, s_{2} = 0, s_{3} \approx 1.546664, s_{4} \approx 2.693623

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