Solve (4x-3)(3x^2-5x-8)

Question

Simplify the expression

12 x^{3} - 29 x^{2} - 17 x + 24

Evaluate

(4 x - 3) (3 x^{2} - 5 x - 8)

Apply the distributive property

4 x \times 3 x^{2} - 4 x \times 5 x - 4 x \times 8 - 3 \times 3 x^{2} - (- 3 \times 5 x) - (- 3 \times 8)

Multiply the terms

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Evaluate

4 x \times 3 x^{2}

Multiply the numbers

12 x \times x^{2}

Multiply the terms

More Steps

Evaluate

x \times x^{2}

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

x^{1 + 2}

Add the numbers

x^{3}

12 x^{3}

12 x^{3} - 4 x \times 5 x - 4 x \times 8 - 3 \times 3 x^{2} - (- 3 \times 5 x) - (- 3 \times 8)

Multiply the terms

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Evaluate

4 x \times 5 x

Multiply the numbers

20 x \times x

Multiply the terms

20 x^{2}

12 x^{3} - 20 x^{2} - 4 x \times 8 - 3 \times 3 x^{2} - (- 3 \times 5 x) - (- 3 \times 8)

Multiply the numbers

12 x^{3} - 20 x^{2} - 32 x - 3 \times 3 x^{2} - (- 3 \times 5 x) - (- 3 \times 8)

Multiply the numbers

12 x^{3} - 20 x^{2} - 32 x - 9 x^{2} - (- 3 \times 5 x) - (- 3 \times 8)

Multiply the numbers

12 x^{3} - 20 x^{2} - 32 x - 9 x^{2} - (- 15 x) - (- 3 \times 8)

Multiply the numbers

12 x^{3} - 20 x^{2} - 32 x - 9 x^{2} - (- 15 x) - (- 24)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

12 x^{3} - 20 x^{2} - 32 x - 9 x^{2} + 15 x + 24

Subtract the terms

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Evaluate

- 20 x^{2} - 9 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(- 20 - 9) x^{2}

Subtract the numbers

- 29 x^{2}

12 x^{3} - 29 x^{2} - 32 x + 15 x + 24

Solution

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Evaluate

- 32 x + 15 x

Collect like terms by calculating the sum or difference of their coefficients

(- 32 + 15) x

Add the numbers

- 17 x

12 x^{3} - 29 x^{2} - 17 x + 24

Show Solution

Factor the expression

(4 x - 3) (x + 1) (3 x - 8)

Evaluate

(4 x - 3) (3 x^{2} - 5 x - 8)

Solution

More Steps

Evaluate

3 x^{2} - 5 x - 8

Rewrite the expression

3 x^{2} + (- 8 + 3) x - 8

Calculate

3 x^{2} - 8 x + 3 x - 8

Rewrite the expression

x \times 3 x - x \times 8 + 3 x - 8

Factor out x from the expression

x (3 x - 8) + 3 x - 8

Factor out 3 x - 8 from the expression

(x + 1) (3 x - 8)

(4 x - 3) (x + 1) (3 x - 8)

Show Solution

Find the roots

x_{1} = - 1, x_{2} = \frac{3}{4}, x_{3} = \frac{8}{3}

Alternative Form

x_{1} = - 1, x_{2} = 0.75, x_{3} = 2. \dot{6}

Evaluate

(4 x - 3) (3 x^{2} - 5 x - 8)

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

(4 x - 3) (3 x^{2} - 5 x - 8) = 0

Separate the equation into 2 possible cases

4 x - 3 = 0 3 x^{2} - 5 x - 8 = 0

Solve the equation

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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} 3 x^{2} - 5 x - 8 = 0

Solve the equation

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Evaluate

3 x^{2} - 5 x - 8 = 0

Factor the expression

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Evaluate

3 x^{2} - 5 x - 8

Rewrite the expression

3 x^{2} + (- 8 + 3) x - 8

Calculate

3 x^{2} - 8 x + 3 x - 8

Rewrite the expression

x \times 3 x - x \times 8 + 3 x - 8

Factor out x from the expression

x (3 x - 8) + 3 x - 8

Factor out 3 x - 8 from the expression

(x + 1) (3 x - 8)

(x + 1) (3 x - 8) = 0

When the product of factors equals 0,at least one factor is 0

x + 1 = 0 3 x - 8 = 0

Solve the equation for x

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Evaluate

x + 1 = 0

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

x = 0 - 1

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

x = - 1

x = - 1 3 x - 8 = 0

Solve the equation for x

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Evaluate

3 x - 8 = 0

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

3 x = 0 + 8

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

3 x = 8

Divide both sides

\frac{3 x}{3} = \frac{8}{3}

Divide the numbers

x = \frac{8}{3}

x = - 1 x = \frac{8}{3}

x = \frac{3}{4} x = - 1 x = \frac{8}{3}

Solution

x_{1} = - 1, x_{2} = \frac{3}{4}, x_{3} = \frac{8}{3}

Alternative Form

x_{1} = - 1, x_{2} = 0.75, x_{3} = 2. \dot{6}

Show Solution