Solve (15x^2 - x - 2)

Question

Factor the expression

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

Evaluate

15 x^{2} - x - 2

Rewrite the expression

15 x^{2} + (- 6 + 5) x - 2

Calculate

15 x^{2} - 6 x + 5 x - 2

Rewrite the expression

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

Factor out 3 x from the expression

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

Solution

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

Show Solution

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0.4

Evaluate

(15 x^{2} - x - 2)

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

15 x^{2} - x - 2 = 0

Factor the expression

More Steps

Evaluate

15 x^{2} - x - 2

Rewrite the expression

15 x^{2} + (- 6 + 5) x - 2

Calculate

15 x^{2} - 6 x + 5 x - 2

Rewrite the expression

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

Factor out 3 x from the expression

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

Factor out 5 x - 2 from the expression

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

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

When the product of factors equals 0,at least one factor is 0

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

Solve the equation for x

More Steps

Evaluate

3 x + 1 = 0

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

3 x = 0 - 1

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

3 x = - 1

Divide both sides

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

Divide the numbers

x = \frac{- 1}{3}

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

x = - \frac{1}{3}

x = - \frac{1}{3} 5 x - 2 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 2 = 0

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

5 x = 0 + 2

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

5 x = 2

Divide both sides

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

Divide the numbers

x = \frac{2}{5}

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

Solution

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0.4

Show Solution