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

Question

Simplify the expression

420 x^{4} - 315 x^{3}

Evaluate

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

Remove the parentheses

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

Multiply the terms

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Evaluate

3 \times 5 \times 7

Multiply the terms

15 \times 7

Multiply the numbers

105

(4 x - 3) \times 105 x^{2} \times x

Multiply the terms with the same base by adding their exponents

(4 x - 3) \times 105 x^{2 + 1}

Add the numbers

(4 x - 3) \times 105 x^{3}

Multiply the terms

105 x^{3} (4 x - 3)

Apply the distributive property

105 x^{3} \times 4 x - 105 x^{3} \times 3

Multiply the terms

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Evaluate

105 x^{3} \times 4 x

Multiply the numbers

420 x^{3} \times x

Multiply the terms

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Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

420 x^{4}

420 x^{4} - 105 x^{3} \times 3

Solution

420 x^{4} - 315 x^{3}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3}{4}

Alternative Form

x_{1} = 0, x_{2} = 0.75

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

3 x^{2} \times 5 x \times 7

Multiply the terms

More Steps

Evaluate

3 \times 5 \times 7

Multiply the terms

15 \times 7

Multiply the numbers

105

105 x^{2} \times x

Multiply the terms with the same base by adding their exponents

105 x^{2 + 1}

Add the numbers

105 x^{3}

(4 x - 3) \times 105 x^{3} = 0

Multiply the terms

105 x^{3} (4 x - 3) = 0

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

x = 0 4 x - 3 = 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 = 0 x = \frac{3}{4}

Solution

x_{1} = 0, x_{2} = \frac{3}{4}

Alternative Form

x_{1} = 0, x_{2} = 0.75

Show Solution