Solve (3x+4)(2x+10)

Question

Simplify the expression

6 x^{2} + 38 x + 40

Evaluate

(3 x + 4) (2 x + 10)

Apply the distributive property

3 x \times 2 x + 3 x \times 10 + 4 \times 2 x + 4 \times 10

Multiply the terms

More Steps

Evaluate

3 x \times 2 x

Multiply the numbers

6 x \times x

Multiply the terms

6 x^{2}

6 x^{2} + 3 x \times 10 + 4 \times 2 x + 4 \times 10

Multiply the numbers

6 x^{2} + 30 x + 4 \times 2 x + 4 \times 10

Multiply the numbers

6 x^{2} + 30 x + 8 x + 4 \times 10

Multiply the numbers

6 x^{2} + 30 x + 8 x + 40

Solution

More Steps

Evaluate

30 x + 8 x

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

(30 + 8) x

Add the numbers

38 x

6 x^{2} + 38 x + 40

Show Solution

Factor the expression

2 (3 x + 4) (x + 5)

Evaluate

(3 x + 4) (2 x + 10)

Factor the expression

(3 x + 4) \times 2 (x + 5)

Solution

2 (3 x + 4) (x + 5)

Show Solution

Find the roots

x_{1} = - 5, x_{2} = - \frac{4}{3}

Alternative Form

x_{1} = - 5, x_{2} = - 1. \dot{3}

Evaluate

(3 x + 4) (2 x + 10)

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

(3 x + 4) (2 x + 10) = 0

Separate the equation into 2 possible cases

3 x + 4 = 0 2 x + 10 = 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}

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

x = - \frac{4}{3}

x = - \frac{4}{3} 2 x + 10 = 0

Solve the equation

More Steps

Evaluate

2 x + 10 = 0

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

2 x = 0 - 10

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

2 x = - 10

Divide both sides

\frac{2 x}{2} = \frac{- 10}{2}

Divide the numbers

x = \frac{- 10}{2}

Divide the numbers

More Steps

Evaluate

\frac{- 10}{2}

Reduce the numbers

\frac{- 5}{1}

Calculate

- 5

x = - 5

x = - \frac{4}{3} x = - 5

Solution

x_{1} = - 5, x_{2} = - \frac{4}{3}

Alternative Form

x_{1} = - 5, x_{2} = - 1. \dot{3}

Show Solution