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

Question

Simplify the expression

6 x^{3} + 22 x^{2} + 16 x - 8

Evaluate

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

Multiply the terms

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

Subtract the terms

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

Any expression multiplied by 0 equals 0

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

Multiply the terms

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

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

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

Simplify

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

Simplify

More Steps

Evaluate

2 (x^{2} + 4 x + 4)

Apply the distributive property

2 x^{2} + 2 \times 4 x + 2 \times 4

Multiply the numbers

2 x^{2} + 8 x + 2 \times 4

Multiply the numbers

2 x^{2} + 8 x + 8

(2 x^{2} + 8 x + 8) (3 x - 1)

Apply the distributive property

2 x^{2} \times 3 x - 2 x^{2} \times 1 + 8 x \times 3 x - 8 x \times 1 + 8 \times 3 x - 8 \times 1

Multiply the terms

More Steps

Evaluate

2 x^{2} \times 3 x

Multiply the numbers

6 x^{2} \times x

Multiply the terms

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Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

6 x^{3}

6 x^{3} - 2 x^{2} \times 1 + 8 x \times 3 x - 8 x \times 1 + 8 \times 3 x - 8 \times 1

Any expression multiplied by 1 remains the same

6 x^{3} - 2 x^{2} + 8 x \times 3 x - 8 x \times 1 + 8 \times 3 x - 8 \times 1

Multiply the terms

More Steps

Evaluate

8 x \times 3 x

Multiply the numbers

24 x \times x

Multiply the terms

24 x^{2}

6 x^{3} - 2 x^{2} + 24 x^{2} - 8 x \times 1 + 8 \times 3 x - 8 \times 1

Any expression multiplied by 1 remains the same

6 x^{3} - 2 x^{2} + 24 x^{2} - 8 x + 8 \times 3 x - 8 \times 1

Multiply the numbers

6 x^{3} - 2 x^{2} + 24 x^{2} - 8 x + 24 x - 8 \times 1

Any expression multiplied by 1 remains the same

6 x^{3} - 2 x^{2} + 24 x^{2} - 8 x + 24 x - 8

Add the terms

More Steps

Evaluate

- 2 x^{2} + 24 x^{2}

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

(- 2 + 24) x^{2}

Add the numbers

22 x^{2}

6 x^{3} + 22 x^{2} - 8 x + 24 x - 8

Solution

More Steps

Evaluate

- 8 x + 24 x

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

(- 8 + 24) x

Add the numbers

16 x

6 x^{3} + 22 x^{2} + 16 x - 8

Show Solution

Find the roots

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

Alternative Form

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

Evaluate

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

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

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

Multiply the terms

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

Subtract the terms

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

Multiply the terms

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

Any expression multiplied by 0 equals 0

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

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

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

(x + 2)^{2} = 0

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

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = - 2 3 x - 1 = 0

Solve the equation

More Steps

Evaluate

3 x - 1 = 0

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

3 x = 0 + 1

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

3 x = 1

Divide both sides

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

Divide the numbers

x = \frac{1}{3}

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

Solution

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

Alternative Form

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

Show Solution