Solve 3x^(2)-x-10

Question

Factor the expression

(x - 2) (3 x + 5)

Evaluate

3 x^{2} - x - 10

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 2 from the expression

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

Solution

(x - 2) (3 x + 5)

Show Solution

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

Alternative Form

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

Evaluate

3 x^{2} - x - 10

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

3 x^{2} - x - 10 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - x - 10

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 2 from the expression

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

Factor out 3 x + 5 from the expression

(x - 2) (3 x + 5)

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

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

x - 2 = 0 3 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 2 3 x + 5 = 0

Solve the equation for x

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}

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

x = - \frac{5}{3}

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

Solution

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

Alternative Form

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

Show Solution