Solve (x-5)(3x+7)

Question

Simplify the expression

3 x^{2} - 8 x - 35

Evaluate

(x - 5) (3 x + 7)

Apply the distributive property

x \times 3 x + x \times 7 - 5 \times 3 x - 5 \times 7

Multiply the terms

More Steps

Evaluate

x \times 3 x

Use the commutative property to reorder the terms

3 x \times x

Multiply the terms

3 x^{2}

3 x^{2} + x \times 7 - 5 \times 3 x - 5 \times 7

Use the commutative property to reorder the terms

3 x^{2} + 7 x - 5 \times 3 x - 5 \times 7

Multiply the numbers

3 x^{2} + 7 x - 15 x - 5 \times 7

Multiply the numbers

3 x^{2} + 7 x - 15 x - 35

Solution

More Steps

Evaluate

7 x - 15 x

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

(7 - 15) x

Subtract the numbers

- 8 x

3 x^{2} - 8 x - 35

Show Solution

x_{1} = - \frac{7}{3}, x_{2} = 5

Alternative Form

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

Evaluate

(x - 5) (3 x + 7)

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

(x - 5) (3 x + 7) = 0

Separate the equation into 2 possible cases

x - 5 = 0 3 x + 7 = 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 3 x + 7 = 0

Solve the equation

More Steps

Evaluate

3 x + 7 = 0

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

3 x = 0 - 7

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

3 x = - 7

Divide both sides

\frac{3 x}{3} = \frac{- 7}{3}

Divide the numbers

x = \frac{- 7}{3}

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

x = - \frac{7}{3}

x = 5 x = - \frac{7}{3}

Solution

x_{1} = - \frac{7}{3}, x_{2} = 5

Alternative Form

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

Show Solution