Solve (2x^2 5x 1)(3x-4)

Question

Simplify the expression

30 x^{4} - 40 x^{3}

Evaluate

(2 x^{2} \times 5 x \times 1) (3 x - 4)

Remove the parentheses

2 x^{2} \times 5 x \times 1 \times (3 x - 4)

Rewrite the expression

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1} (3 x - 4)

Add the numbers

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

Apply the distributive property

10 x^{3} \times 3 x - 10 x^{3} \times 4

Multiply the terms

More Steps

Evaluate

10 x^{3} \times 3 x

Multiply the numbers

30 x^{3} \times x

Multiply the terms

More Steps

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}

30 x^{4}

30 x^{4} - 10 x^{3} \times 4

Solution

30 x^{4} - 40 x^{3}

Show Solution

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

Alternative Form

x_{1} = 0, x_{2} = 1. \dot{3}

Evaluate

(2 x^{2} \times 5 x \times 1) (3 x - 4)

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

(2 x^{2} \times 5 x \times 1) (3 x - 4) = 0

Multiply the terms

More Steps

Multiply the terms

2 x^{2} \times 5 x \times 1

Rewrite the expression

2 x^{2} \times 5 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

x = 0 3 x - 4 = 0

Solve the equation

More Steps

Evaluate

3 x - 4 = 0

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

3 x = 0 + 4

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

3 x = 4

Divide both sides

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

Divide the numbers

x = \frac{4}{3}

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

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 1. \dot{3}

Show Solution