Solve (3x + 4)(3x - 5)

Question

Simplify the expression

9 x^{2} - 3 x - 20

Evaluate

(3 x + 4) (3 x - 5)

Apply the distributive property

3 x \times 3 x - 3 x \times 5 + 4 \times 3 x - 4 \times 5

Multiply the terms

More Steps

Evaluate

3 x \times 3 x

Multiply the numbers

9 x \times x

Multiply the terms

9 x^{2}

9 x^{2} - 3 x \times 5 + 4 \times 3 x - 4 \times 5

Multiply the numbers

9 x^{2} - 15 x + 4 \times 3 x - 4 \times 5

Multiply the numbers

9 x^{2} - 15 x + 12 x - 4 \times 5

Multiply the numbers

9 x^{2} - 15 x + 12 x - 20

Solution

More Steps

Evaluate

- 15 x + 12 x

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

(- 15 + 12) x

Add the numbers

- 3 x

9 x^{2} - 3 x - 20

Show Solution

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

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 1. \dot{6}

Evaluate

(3 x + 4) (3 x - 5)

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

(3 x + 4) (3 x - 5) = 0

Separate the equation into 2 possible cases

3 x + 4 = 0 3 x - 5 = 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} 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{4}{3} x = \frac{5}{3}

Solution

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

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 1. \dot{6}

Show Solution