Solve -6x(2x-3(x-1) 4x)

Question

Simplify the expression

- 84 x^{2} + 72 x^{3}

Evaluate

- 6 x (2 x - 3 (x - 1) \times 4 x)

Multiply

More Steps

Multiply the terms

3 (x - 1) \times 4 x

Multiply the terms

12 (x - 1) x

Multiply the terms

12 x (x - 1)

- 6 x (2 x - 12 x (x - 1))

Subtract the terms

More Steps

Simplify

2 x - 12 x (x - 1)

Expand the expression

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Calculate

- 12 x (x - 1)

Apply the distributive property

- 12 x \times x - (- 12 x \times 1)

Multiply the terms

- 12 x^{2} - (- 12 x \times 1)

Any expression multiplied by 1 remains the same

- 12 x^{2} - (- 12 x)

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^{2} + 12 x

2 x - 12 x^{2} + 12 x

Add the terms

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Evaluate

2 x + 12 x

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

(2 + 12) x

Add the numbers

14 x

14 x - 12 x^{2}

- 6 x (14 x - 12 x^{2})

Apply the distributive property

- 6 x \times 14 x - (- 6 x \times 12 x^{2})

Multiply the terms

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Evaluate

- 6 x \times 14 x

Multiply the numbers

- 84 x \times x

Multiply the terms

- 84 x^{2}

- 84 x^{2} - (- 6 x \times 12 x^{2})

Multiply the terms

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Evaluate

- 6 x \times 12 x^{2}

Multiply the numbers

- 72 x \times x^{2}

Multiply the terms

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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}

- 72 x^{3}

- 84 x^{2} - (- 72 x^{3})

Solution

- 84 x^{2} + 72 x^{3}

Show Solution

Factor the expression

- 12 x^{2} (7 - 6 x)

Evaluate

- 6 x (2 x - 3 (x - 1) \times 4 x)

Multiply

More Steps

Evaluate

3 (x - 1) \times 4 x

Multiply the terms

12 (x - 1) x

Multiply the terms

12 x (x - 1)

- 6 x (2 x - 12 x (x - 1))

Factor the expression

More Steps

Evaluate

2 x - 12 x (x - 1)

Rewrite the expression

2 x - 2 x \times 6 (x - 1)

Factor out 2 x from the expression

2 x (1 - 6 (x - 1))

Calculate

2 x (7 - 6 x)

- 6 x \times 2 x (7 - 6 x)

Solution

- 12 x^{2} (7 - 6 x)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{7}{6}

Alternative Form

x_{1} = 0, x_{2} = 1.1 \dot{6}

Evaluate

- 6 x (2 x - 3 (x - 1) \times 4 x)

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

- 6 x (2 x - 3 (x - 1) \times 4 x) = 0

Multiply

More Steps

Multiply the terms

3 (x - 1) \times 4 x

Multiply the terms

12 (x - 1) x

Multiply the terms

12 x (x - 1)

- 6 x (2 x - 12 x (x - 1)) = 0

Subtract the terms

More Steps

Simplify

2 x - 12 x (x - 1)

Expand the expression

More Steps

Calculate

- 12 x (x - 1)

Apply the distributive property

- 12 x \times x - (- 12 x \times 1)

Multiply the terms

- 12 x^{2} - (- 12 x \times 1)

Any expression multiplied by 1 remains the same

- 12 x^{2} - (- 12 x)

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^{2} + 12 x

2 x - 12 x^{2} + 12 x

Add the terms

More Steps

Evaluate

2 x + 12 x

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

(2 + 12) x

Add the numbers

14 x

14 x - 12 x^{2}

- 6 x (14 x - 12 x^{2}) = 0

Change the sign

6 x (14 x - 12 x^{2}) = 0

Elimination the left coefficient

x (14 x - 12 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 14 x - 12 x^{2} = 0

Solve the equation

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Evaluate

14 x - 12 x^{2} = 0

Factor the expression

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Evaluate

14 x - 12 x^{2}

Rewrite the expression

2 x \times 7 - 2 x \times 6 x

Factor out 2 x from the expression

2 x (7 - 6 x)

2 x (7 - 6 x) = 0

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

2 x = 0 7 - 6 x = 0

Solve the equation for x

x = 0 7 - 6 x = 0

Solve the equation for x

More Steps

Evaluate

7 - 6 x = 0

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

- 6 x = 0 - 7

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

- 6 x = - 7

Change the signs on both sides of the equation

6 x = 7

Divide both sides

\frac{6 x}{6} = \frac{7}{6}

Divide the numbers

x = \frac{7}{6}

x = 0 x = \frac{7}{6}

x = 0 x = 0 x = \frac{7}{6}

Find the union

x = 0 x = \frac{7}{6}

Solution

x_{1} = 0, x_{2} = \frac{7}{6}

Alternative Form

x_{1} = 0, x_{2} = 1.1 \dot{6}

Show Solution