Solve 12x^2-7x-10

Question

Factor the expression

(3 x + 2) (4 x - 5)

Evaluate

12 x^{2} - 7 x - 10

Rewrite the expression

12 x^{2} + (- 15 + 8) x - 10

Calculate

12 x^{2} - 15 x + 8 x - 10

Rewrite the expression

3 x \times 4 x - 3 x \times 5 + 2 \times 4 x - 2 \times 5

Factor out 3 x from the expression

3 x (4 x - 5) + 2 \times 4 x - 2 \times 5

Factor out 2 from the expression

3 x (4 x - 5) + 2 (4 x - 5)

Solution

(3 x + 2) (4 x - 5)

Show Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 1.25

Evaluate

12 x^{2} - 7 x - 10

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

12 x^{2} - 7 x - 10 = 0

Factor the expression

More Steps

Evaluate

12 x^{2} - 7 x - 10

Rewrite the expression

12 x^{2} + (- 15 + 8) x - 10

Calculate

12 x^{2} - 15 x + 8 x - 10

Rewrite the expression

3 x \times 4 x - 3 x \times 5 + 2 \times 4 x - 2 \times 5

Factor out 3 x from the expression

3 x (4 x - 5) + 2 \times 4 x - 2 \times 5

Factor out 2 from the expression

3 x (4 x - 5) + 2 (4 x - 5)

Factor out 4 x - 5 from the expression

(3 x + 2) (4 x - 5)

(3 x + 2) (4 x - 5) = 0

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

3 x + 2 = 0 4 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 2 = 0

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

3 x = 0 - 2

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

3 x = - 2

Divide both sides

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

Divide the numbers

x = \frac{- 2}{3}

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

x = - \frac{2}{3}

x = - \frac{2}{3} 4 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

4 x - 5 = 0

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

4 x = 0 + 5

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

4 x = 5

Divide both sides

\frac{4 x}{4} = \frac{5}{4}

Divide the numbers

x = \frac{5}{4}

x = - \frac{2}{3} x = \frac{5}{4}

Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 1.25

Show Solution