Solve (2x+1)(3x+2)

Question

Simplify the expression

6 x^{2} + 7 x + 2

Evaluate

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

Apply the distributive property

2 x \times 3 x + 2 x \times 2 + 1 \times 3 x + 1 \times 2

Multiply the terms

More Steps

Evaluate

2 x \times 3 x

Multiply the numbers

6 x \times x

Multiply the terms

6 x^{2}

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

Multiply the numbers

6 x^{2} + 4 x + 1 \times 3 x + 1 \times 2

Any expression multiplied by 1 remains the same

6 x^{2} + 4 x + 3 x + 1 \times 2

Any expression multiplied by 1 remains the same

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

Solution

More Steps

Evaluate

4 x + 3 x

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

(4 + 3) x

Add the numbers

7 x

6 x^{2} + 7 x + 2

Show Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = - 0.5

Evaluate

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

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

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

Separate the equation into 2 possible cases

2 x + 1 = 0 3 x + 2 = 0

Solve the equation

More Steps

Evaluate

2 x + 1 = 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

Divide both sides

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

Divide the numbers

x = \frac{- 1}{2}

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

x = - \frac{1}{2}

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

Solve the equation

More Steps

Evaluate

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

Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = - 0.5

Show Solution