Solve (4x-3)(3x^2 5x-7)

Question

Simplify the expression

60 x^{4} - 28 x - 45 x^{3} + 21

Evaluate

(4 x - 3) (3 x^{2} \times 5 x - 7)

Multiply

More Steps

Evaluate

3 x^{2} \times 5 x

Multiply the terms

15 x^{2} \times x

Multiply the terms with the same base by adding their exponents

15 x^{2 + 1}

Add the numbers

15 x^{3}

(4 x - 3) (15 x^{3} - 7)

Apply the distributive property

4 x \times 15 x^{3} - 4 x \times 7 - 3 \times 15 x^{3} - (- 3 \times 7)

Multiply the terms

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Evaluate

4 x \times 15 x^{3}

Multiply the numbers

60 x \times x^{3}

Multiply the terms

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Evaluate

x \times x^{3}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 3}

Add the numbers

x^{4}

60 x^{4}

60 x^{4} - 4 x \times 7 - 3 \times 15 x^{3} - (- 3 \times 7)

Multiply the numbers

60 x^{4} - 28 x - 3 \times 15 x^{3} - (- 3 \times 7)

Multiply the numbers

60 x^{4} - 28 x - 45 x^{3} - (- 3 \times 7)

Multiply the numbers

60 x^{4} - 28 x - 45 x^{3} - (- 21)

Solution

60 x^{4} - 28 x - 45 x^{3} + 21

Show Solution

Find the roots

x_{1} = \frac{3}{4}, x_{2} = \frac{3 1575}{15}

Alternative Form

x_{1} = 0.75, x_{2} \approx 0.775656

Evaluate

(4 x - 3) (3 x^{2} \times 5 x - 7)

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

(4 x - 3) (3 x^{2} \times 5 x - 7) = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 5 x

Multiply the terms

15 x^{2} \times x

Multiply the terms with the same base by adding their exponents

15 x^{2 + 1}

Add the numbers

15 x^{3}

(4 x - 3) (15 x^{3} - 7) = 0

Separate the equation into 2 possible cases

4 x - 3 = 0 15 x^{3} - 7 = 0

Solve the equation

More Steps

Evaluate

4 x - 3 = 0

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

4 x = 0 + 3

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

4 x = 3

Divide both sides

\frac{4 x}{4} = \frac{3}{4}

Divide the numbers

x = \frac{3}{4}

x = \frac{3}{4} 15 x^{3} - 7 = 0

Solve the equation

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Evaluate

15 x^{3} - 7 = 0

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

15 x^{3} = 0 + 7

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

15 x^{3} = 7

Divide both sides

\frac{15 x ^{3}}{15} = \frac{7}{15}

Divide the numbers

x^{3} = \frac{7}{15}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{7}{15}

Calculate

x = 3 \frac{7}{15}

Simplify the root

More Steps

Evaluate

3 \frac{7}{15}

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

\frac{3 7}{3 15}

Multiply by the Conjugate

\frac{3 7 \times 3 1 5 ^{2}}{3 15 \times 3 1 5 ^{2}}

Simplify

\frac{3 7 \times 3 225}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

\frac{3 1575}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

\frac{3 1575}{15}

x = \frac{3 1575}{15}

x = \frac{3}{4} x = \frac{3 1575}{15}

Solution

x_{1} = \frac{3}{4}, x_{2} = \frac{3 1575}{15}

Alternative Form

x_{1} = 0.75, x_{2} \approx 0.775656

Show Solution