Solve 3(2+3x)-(5+2x)(2+3x)

Question

Simplify the expression

- 4 - 10 x - 6 x^{2}

Evaluate

3 (2 + 3 x) - (5 + 2 x) (2 + 3 x)

Rewrite the expression

3 (2 + 3 x) + (- 5 - 2 x) (2 + 3 x)

Expand the expression

More Steps

Calculate

3 (2 + 3 x)

Apply the distributive property

3 \times 2 + 3 \times 3 x

Multiply the numbers

6 + 3 \times 3 x

Multiply the numbers

6 + 9 x

6 + 9 x + (- 5 - 2 x) (2 + 3 x)

Expand the expression

More Steps

Calculate

(- 5 - 2 x) (2 + 3 x)

Apply the distributive property

- 5 \times 2 - 5 \times 3 x - 2 x \times 2 - 2 x \times 3 x

Multiply the numbers

- 10 - 5 \times 3 x - 2 x \times 2 - 2 x \times 3 x

Multiply the numbers

- 10 - 15 x - 2 x \times 2 - 2 x \times 3 x

Multiply the numbers

- 10 - 15 x - 4 x - 2 x \times 3 x

Multiply the terms

More Steps

Evaluate

- 2 x \times 3 x

Multiply the numbers

- 6 x \times x

Multiply the terms

- 6 x^{2}

- 10 - 15 x - 4 x - 6 x^{2}

Subtract the terms

More Steps

Evaluate

- 15 x - 4 x

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

(- 15 - 4) x

Subtract the numbers

- 19 x

- 10 - 19 x - 6 x^{2}

6 + 9 x - 10 - 19 x - 6 x^{2}

Subtract the numbers

- 4 + 9 x - 19 x - 6 x^{2}

Solution

More Steps

Evaluate

9 x - 19 x

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

(9 - 19) x

Subtract the numbers

- 10 x

- 4 - 10 x - 6 x^{2}

Show Solution

Factor the expression

- 2 (1 + x) (2 + 3 x)

Evaluate

3 (2 + 3 x) - (5 + 2 x) (2 + 3 x)

Rewrite the expression

3 (2 + 3 x) + (- 5 - 2 x) (2 + 3 x)

Factor out 2 + 3 x from the expression

(3 - 5 - 2 x) (2 + 3 x)

Solution

More Steps

Evaluate

3 - 5 - 2 x

Subtract the numbers

- 2 - 2 x

Factor the expression

- 2 (1 + x)

- 2 (1 + x) (2 + 3 x)

Show Solution

Find the roots

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

Alternative Form

x_{1} = - 1, x_{2} = - 0. \dot{6}

Evaluate

3 (2 + 3 x) - (5 + 2 x) (2 + 3 x)

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

3 (2 + 3 x) - (5 + 2 x) (2 + 3 x) = 0

Rewrite the expression

3 (2 + 3 x) + (- 5 - 2 x) (2 + 3 x) = 0

Calculate

More Steps

Evaluate

3 (2 + 3 x) + (- 5 - 2 x) (2 + 3 x)

Expand the expression

More Steps

Calculate

3 (2 + 3 x)

Apply the distributive property

3 \times 2 + 3 \times 3 x

Multiply the numbers

6 + 3 \times 3 x

Multiply the numbers

6 + 9 x

6 + 9 x + (- 5 - 2 x) (2 + 3 x)

Expand the expression

More Steps

Calculate

(- 5 - 2 x) (2 + 3 x)

Apply the distributive property

- 5 \times 2 - 5 \times 3 x - 2 x \times 2 - 2 x \times 3 x

Multiply the numbers

- 10 - 5 \times 3 x - 2 x \times 2 - 2 x \times 3 x

Multiply the numbers

- 10 - 15 x - 2 x \times 2 - 2 x \times 3 x

Multiply the numbers

- 10 - 15 x - 4 x - 2 x \times 3 x

Multiply the terms

- 10 - 15 x - 4 x - 6 x^{2}

Subtract the terms

- 10 - 19 x - 6 x^{2}

6 + 9 x - 10 - 19 x - 6 x^{2}

Subtract the numbers

- 4 + 9 x - 19 x - 6 x^{2}

Subtract the terms

More Steps

Evaluate

9 x - 19 x

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

(9 - 19) x

Subtract the numbers

- 10 x

- 4 - 10 x - 6 x^{2}

- 4 - 10 x - 6 x^{2} = 0

Factor the expression

More Steps

Evaluate

- 4 - 10 x - 6 x^{2}

Rewrite the expression

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

Factor out - 2 from the expression

- 2 (2 + 5 x + 3 x^{2})

Factor the expression

More Steps

Evaluate

2 + 5 x + 3 x^{2}

Rewrite the expression

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

Calculate

2 + 3 x + 2 x + 3 x^{2}

Rewrite the expression

2 + 3 x + x \times 2 + x \times 3 x

Factor out x from the expression

2 + 3 x + x (2 + 3 x)

Factor out 2 + 3 x from the expression

(1 + x) (2 + 3 x)

- 2 (1 + x) (2 + 3 x)

- 2 (1 + x) (2 + 3 x) = 0

Divide the terms

(1 + x) (2 + 3 x) = 0

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

1 + x = 0 2 + 3 x = 0

Solve the equation for x

More Steps

Evaluate

1 + x = 0

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

x = 0 - 1

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

x = - 1

x = - 1 2 + 3 x = 0

Solve the equation for x

More Steps

Evaluate

2 + 3 x = 0

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

3 x = 0 - 2

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

3 x = - 2

Divide both sides

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

Divide the numbers

x = \frac{- 2}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{2}{3}

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

Solution

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

Alternative Form

x_{1} = - 1, x_{2} = - 0. \dot{6}

Show Solution