Solve "3x^6" 5x^5 6x^4 79x^3 -8x^2 3x 12

Question

Simplify the expression

2370 x^{12} - 288 x^{3}

Evaluate

5 x^{5} \times 6 x^{4} \times 79 x^{3} - 8 x^{2} \times 3 x \times 12

Multiply

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Multiply the terms

5 x^{5} \times 6 x^{4} \times 79 x^{3}

Multiply the terms

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Evaluate

5 \times 6 \times 79

Multiply the terms

30 \times 79

Multiply the numbers

2370

2370 x^{5} \times x^{4} \times x^{3}

Multiply the terms with the same base by adding their exponents

2370 x^{5 + 4 + 3}

Add the numbers

2370 x^{12}

2370 x^{12} - 8 x^{2} \times 3 x \times 12

Solution

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Multiply the terms

8 x^{2} \times 3 x \times 12

Multiply the terms

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Evaluate

8 \times 3 \times 12

Multiply the terms

24 \times 12

Multiply the numbers

288

288 x^{2} \times x

Multiply the terms with the same base by adding their exponents

288 x^{2 + 1}

Add the numbers

288 x^{3}

2370 x^{12} - 288 x^{3}

Show Solution

Factor the expression

6 x^{3} (395 x^{9} - 48)

Evaluate

5 x^{5} \times 6 x^{4} \times 79 x^{3} - 8 x^{2} \times 3 x \times 12

Multiply

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Multiply the terms

5 x^{5} \times 6 x^{4} \times 79 x^{3}

Multiply the terms

More Steps

Evaluate

5 \times 6 \times 79

Multiply the terms

30 \times 79

Multiply the numbers

2370

2370 x^{5} \times x^{4} \times x^{3}

Multiply the terms with the same base by adding their exponents

2370 x^{5 + 4 + 3}

Add the numbers

2370 x^{12}

2370 x^{12} - 8 x^{2} \times 3 x \times 12

Multiply

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Multiply the terms

8 x^{2} \times 3 x \times 12

Multiply the terms

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Evaluate

8 \times 3 \times 12

Multiply the terms

24 \times 12

Multiply the numbers

288

288 x^{2} \times x

Multiply the terms with the same base by adding their exponents

288 x^{2 + 1}

Add the numbers

288 x^{3}

2370 x^{12} - 288 x^{3}

Rewrite the expression

6 x^{3} \times 395 x^{9} - 6 x^{3} \times 48

Solution

6 x^{3} (395 x^{9} - 48)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{9 48 \times 39 5 ^{8}}{395}

Alternative Form

x_{1} = 0, x_{2} \approx 0.791214

Evaluate

5 x^{5} \times 6 x^{4} \times 79 x^{3} - 8 x^{2} \times 3 x \times 12

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

5 x^{5} \times 6 x^{4} \times 79 x^{3} - 8 x^{2} \times 3 x \times 12 = 0

Multiply

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Multiply the terms

5 x^{5} \times 6 x^{4} \times 79 x^{3}

Multiply the terms

More Steps

Evaluate

5 \times 6 \times 79

Multiply the terms

30 \times 79

Multiply the numbers

2370

2370 x^{5} \times x^{4} \times x^{3}

Multiply the terms with the same base by adding their exponents

2370 x^{5 + 4 + 3}

Add the numbers

2370 x^{12}

2370 x^{12} - 8 x^{2} \times 3 x \times 12 = 0

Multiply

More Steps

Multiply the terms

8 x^{2} \times 3 x \times 12

Multiply the terms

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Evaluate

8 \times 3 \times 12

Multiply the terms

24 \times 12

Multiply the numbers

288

288 x^{2} \times x

Multiply the terms with the same base by adding their exponents

288 x^{2 + 1}

Add the numbers

288 x^{3}

2370 x^{12} - 288 x^{3} = 0

Factor the expression

6 x^{3} (395 x^{9} - 48) = 0

Divide both sides

x^{3} (395 x^{9} - 48) = 0

Separate the equation into 2 possible cases

x^{3} = 0 395 x^{9} - 48 = 0

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

x = 0 395 x^{9} - 48 = 0

Solve the equation

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Evaluate

395 x^{9} - 48 = 0

Move the constant to the right-hand side and change its sign

395 x^{9} = 0 + 48

Removing 0 doesn't change the value,so remove it from the expression

395 x^{9} = 48

Divide both sides

\frac{395 x ^{9}}{395} = \frac{48}{395}

Divide the numbers

x^{9} = \frac{48}{395}

Take the 9 -th root on both sides of the equation

9 x^{9} = 9 \frac{48}{395}

Calculate

x = 9 \frac{48}{395}

Simplify the root

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Evaluate

9 \frac{48}{395}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{9 48}{9 395}

Multiply by the Conjugate

\frac{9 48 \times 9 39 5 ^{8}}{9 395 \times 9 39 5 ^{8}}

The product of roots with the same index is equal to the root of the product

\frac{9 48 \times 39 5 ^{8}}{9 395 \times 9 39 5 ^{8}}

Multiply the numbers

\frac{9 48 \times 39 5 ^{8}}{395}

x = \frac{9 48 \times 39 5 ^{8}}{395}

x = 0 x = \frac{9 48 \times 39 5 ^{8}}{395}

Solution

x_{1} = 0, x_{2} = \frac{9 48 \times 39 5 ^{8}}{395}

Alternative Form

x_{1} = 0, x_{2} \approx 0.791214

Show Solution