Solve 16x^2-20x-6

Question

Factor the expression

2 (2 x - 3) (4 x + 1)

Evaluate

16 x^{2} - 20 x - 6

Rewrite the expression

2 \times 8 x^{2} - 2 \times 10 x - 2 \times 3

Factor out 2 from the expression

2 (8 x^{2} - 10 x - 3)

Solution

More Steps

Evaluate

8 x^{2} - 10 x - 3

Rewrite the expression

8 x^{2} + (2 - 12) x - 3

Calculate

8 x^{2} + 2 x - 12 x - 3

Rewrite the expression

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

Factor out 2 x from the expression

2 x (4 x + 1) - 3 \times 4 x - 3

Factor out - 3 from the expression

2 x (4 x + 1) - 3 (4 x + 1)

Factor out 4 x + 1 from the expression

(2 x - 3) (4 x + 1)

2 (2 x - 3) (4 x + 1)

Show Solution

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

Alternative Form

x_{1} = - 0.25, x_{2} = 1.5

Evaluate

16 x^{2} - 20 x - 6

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

16 x^{2} - 20 x - 6 = 0

Factor the expression

More Steps

Evaluate

16 x^{2} - 20 x - 6

Rewrite the expression

2 \times 8 x^{2} - 2 \times 10 x - 2 \times 3

Factor out 2 from the expression

2 (8 x^{2} - 10 x - 3)

Factor the expression

More Steps

Evaluate

8 x^{2} - 10 x - 3

Rewrite the expression

8 x^{2} + (2 - 12) x - 3

Calculate

8 x^{2} + 2 x - 12 x - 3

Rewrite the expression

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

Factor out 2 x from the expression

2 x (4 x + 1) - 3 \times 4 x - 3

Factor out - 3 from the expression

2 x (4 x + 1) - 3 (4 x + 1)

Factor out 4 x + 1 from the expression

(2 x - 3) (4 x + 1)

2 (2 x - 3) (4 x + 1)

2 (2 x - 3) (4 x + 1) = 0

Divide the terms

(2 x - 3) (4 x + 1) = 0

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

2 x - 3 = 0 4 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

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

Divide the numbers

x = \frac{3}{2}

x = \frac{3}{2} 4 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

4 x + 1 = 0

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

4 x = 0 - 1

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

4 x = - 1

Divide both sides

\frac{4 x}{4} = \frac{- 1}{4}

Divide the numbers

x = \frac{- 1}{4}

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

x = - \frac{1}{4}

x = \frac{3}{2} x = - \frac{1}{4}

Solution

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

Alternative Form

x_{1} = - 0.25, x_{2} = 1.5

Show Solution