Solve (4y - 3)(2y^23y - 5)

Question

Simplify the expression

24 y^{4} - 20 y - 18 y^{3} + 15

Evaluate

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

Multiply

More Steps

Evaluate

2 y^{2} \times 3 y

Multiply the terms

6 y^{2} \times y

Multiply the terms with the same base by adding their exponents

6 y^{2 + 1}

Add the numbers

6 y^{3}

(4 y - 3) (6 y^{3} - 5)

Apply the distributive property

4 y \times 6 y^{3} - 4 y \times 5 - 3 \times 6 y^{3} - (- 3 \times 5)

Multiply the terms

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Evaluate

4 y \times 6 y^{3}

Multiply the numbers

24 y \times y^{3}

Multiply the terms

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Evaluate

y \times y^{3}

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

y^{1 + 3}

Add the numbers

y^{4}

24 y^{4}

24 y^{4} - 4 y \times 5 - 3 \times 6 y^{3} - (- 3 \times 5)

Multiply the numbers

24 y^{4} - 20 y - 3 \times 6 y^{3} - (- 3 \times 5)

Multiply the numbers

24 y^{4} - 20 y - 18 y^{3} - (- 3 \times 5)

Multiply the numbers

24 y^{4} - 20 y - 18 y^{3} - (- 15)

Solution

24 y^{4} - 20 y - 18 y^{3} + 15

Show Solution

Find the roots

y_{1} = \frac{3}{4}, y_{2} = \frac{3 180}{6}

Alternative Form

y_{1} = 0.75, y_{2} \approx 0.941036

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

2 y^{2} \times 3 y

Multiply the terms

6 y^{2} \times y

Multiply the terms with the same base by adding their exponents

6 y^{2 + 1}

Add the numbers

6 y^{3}

(4 y - 3) (6 y^{3} - 5) = 0

Separate the equation into 2 possible cases

4 y - 3 = 0 6 y^{3} - 5 = 0

Solve the equation

More Steps

Evaluate

4 y - 3 = 0

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

4 y = 0 + 3

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

4 y = 3

Divide both sides

\frac{4 y}{4} = \frac{3}{4}

Divide the numbers

y = \frac{3}{4}

y = \frac{3}{4} 6 y^{3} - 5 = 0

Solve the equation

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Evaluate

6 y^{3} - 5 = 0

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

6 y^{3} = 0 + 5

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

6 y^{3} = 5

Divide both sides

\frac{6 y ^{3}}{6} = \frac{5}{6}

Divide the numbers

y^{3} = \frac{5}{6}

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

3 y^{3} = 3 \frac{5}{6}

Calculate

y = 3 \frac{5}{6}

Simplify the root

More Steps

Evaluate

3 \frac{5}{6}

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

\frac{3 5}{3 6}

Multiply by the Conjugate

\frac{3 5 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{3 5 \times 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{3 180}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{3 180}{6}

y = \frac{3 180}{6}

y = \frac{3}{4} y = \frac{3 180}{6}

Solution

y_{1} = \frac{3}{4}, y_{2} = \frac{3 180}{6}

Alternative Form

y_{1} = 0.75, y_{2} \approx 0.941036

Show Solution