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

Question

Simplify the expression

2 x^{2} + 7 x - 15

Evaluate

(x + 5) (2 x - 3)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x \times 2 x

Use the commutative property to reorder the terms

2 x \times x

Multiply the terms

2 x^{2}

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

Use the commutative property to reorder the terms

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

Multiply the numbers

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

Multiply the numbers

2 x^{2} - 3 x + 10 x - 15

Solution

More Steps

Evaluate

- 3 x + 10 x

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

(- 3 + 10) x

Add the numbers

7 x

2 x^{2} + 7 x - 15

Show Solution

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

Alternative Form

x_{1} = - 5, x_{2} = 1.5

Evaluate

(x + 5) (2 x - 3)

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

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

Separate the equation into 2 possible cases

x + 5 = 0 2 x - 3 = 0

Solve the equation

More Steps

Evaluate

x + 5 = 0

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

x = 0 - 5

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

x = - 5

x = - 5 2 x - 3 = 0

Solve the equation

More Steps

Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

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

Divide the numbers

x = \frac{3}{2}

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

Solution

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

Alternative Form

x_{1} = - 5, x_{2} = 1.5

Show Solution