Solve 30x^2 - 4x - 16

Question

Factor the expression

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

Evaluate

30 x^{2} - 4 x - 16

Rewrite the expression

2 \times 15 x^{2} - 2 \times 2 x - 2 \times 8

Factor out 2 from the expression

2 (15 x^{2} - 2 x - 8)

Solution

More Steps

Evaluate

15 x^{2} - 2 x - 8

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out 3 x from the expression

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

Factor out 2 from the expression

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

Factor out 5 x - 4 from the expression

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

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

Show Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0.8

Evaluate

30 x^{2} - 4 x - 16

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

30 x^{2} - 4 x - 16 = 0

Factor the expression

More Steps

Evaluate

30 x^{2} - 4 x - 16

Rewrite the expression

2 \times 15 x^{2} - 2 \times 2 x - 2 \times 8

Factor out 2 from the expression

2 (15 x^{2} - 2 x - 8)

Factor the expression

More Steps

Evaluate

15 x^{2} - 2 x - 8

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out 3 x from the expression

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

Factor out 2 from the expression

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

Factor out 5 x - 4 from the expression

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

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

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

Divide the terms

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

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

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

Solve the equation for x

More Steps

Evaluate

5 x - 4 = 0

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

5 x = 0 + 4

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

5 x = 4

Divide both sides

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

Divide the numbers

x = \frac{4}{5}

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

Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0.8

Show Solution