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

Question

Simplify the expression

2 x^{3} - 4 x^{4} - 3 + 6 x

Evaluate

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

Multiply

More Steps

Evaluate

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

(2 x^{3} - 3) (1 - 2 x)

Apply the distributive property

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Evaluate

2 x^{3} \times 2 x

Multiply the numbers

4 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}

4 x^{4}

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

Any expression multiplied by 1 remains the same

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

Multiply the numbers

2 x^{3} - 4 x^{4} - 3 - (- 6 x)

Solution

2 x^{3} - 4 x^{4} - 3 + 6 x

Show Solution

Find the roots

x_{1} = \frac{1}{2}, x_{2} = \frac{3 12}{2}

Alternative Form

x_{1} = 0.5, x_{2} \approx 1.144714

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

(2 x^{3} - 3) (1 - 2 x) = 0

Separate the equation into 2 possible cases

2 x^{3} - 3 = 0 1 - 2 x = 0

Solve the equation

More Steps

Evaluate

2 x^{3} - 3 = 0

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

2 x^{3} = 0 + 3

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

2 x^{3} = 3

Divide both sides

\frac{2 x ^{3}}{2} = \frac{3}{2}

Divide the numbers

x^{3} = \frac{3}{2}

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

3 x^{3} = 3 \frac{3}{2}

Calculate

x = 3 \frac{3}{2}

Simplify the root

More Steps

Evaluate

3 \frac{3}{2}

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

\frac{3 3}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 3 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

\frac{3 12}{3 2 \times 3 2 ^{2}}

Multiply the numbers

\frac{3 12}{2}

x = \frac{3 12}{2}

x = \frac{3 12}{2} 1 - 2 x = 0

Solve the equation

More Steps

Evaluate

1 - 2 x = 0

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

- 2 x = 0 - 1

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

- 2 x = - 1

Change the signs on both sides of the equation

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = \frac{3 12}{2} x = \frac{1}{2}

Solution

x_{1} = \frac{1}{2}, x_{2} = \frac{3 12}{2}

Alternative Form

x_{1} = 0.5, x_{2} \approx 1.144714

Show Solution