Solve (2x+1)(3x-5)

Question

Simplify the expression

6 x^{2} - 7 x - 5

Evaluate

(2 x + 1) (3 x - 5)

Apply the distributive property

2 x \times 3 x - 2 x \times 5 + 1 \times 3 x - 1 \times 5

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 5 + 1 \times 3 x - 1 \times 5

Multiply the numbers

6 x^{2} - 10 x + 1 \times 3 x - 1 \times 5

Any expression multiplied by 1 remains the same

6 x^{2} - 10 x + 3 x - 1 \times 5

Any expression multiplied by 1 remains the same

6 x^{2} - 10 x + 3 x - 5

Solution

More Steps

Evaluate

- 10 x + 3 x

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

(- 10 + 3) x

Add the numbers

- 7 x

6 x^{2} - 7 x - 5

Show Solution

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

Alternative Form

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

Evaluate

(2 x + 1) (3 x - 5)

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

(2 x + 1) (3 x - 5) = 0

Separate the equation into 2 possible cases

2 x + 1 = 0 3 x - 5 = 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 - 5 = 0

Solve the equation

More Steps

Evaluate

3 x - 5 = 0

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

3 x = 0 + 5

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

3 x = 5

Divide both sides

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

Divide the numbers

x = \frac{5}{3}

x = - \frac{1}{2} x = \frac{5}{3}

Solution

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

Alternative Form

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

Show Solution