Solve -126x^2-75x-9

Question

Factor the expression

- 3 (6 x + 1) (7 x + 3)

Evaluate

- 126 x^{2} - 75 x - 9

Rewrite the expression

- 3 \times 42 x^{2} - 3 \times 25 x - 3 \times 3

Factor out - 3 from the expression

- 3 (42 x^{2} + 25 x + 3)

Solution

More Steps

Evaluate

42 x^{2} + 25 x + 3

Rewrite the expression

42 x^{2} + (18 + 7) x + 3

Calculate

42 x^{2} + 18 x + 7 x + 3

Rewrite the expression

6 x \times 7 x + 6 x \times 3 + 7 x + 3

Factor out 6 x from the expression

6 x (7 x + 3) + 7 x + 3

Factor out 7 x + 3 from the expression

(6 x + 1) (7 x + 3)

- 3 (6 x + 1) (7 x + 3)

Show Solution

x_{1} = - \frac{3}{7}, x_{2} = - \frac{1}{6}

Alternative Form

x_{1} = - 0. \dot{4} 2857 \dot{1}, x_{2} = - 0.1 \dot{6}

Evaluate

- 126 x^{2} - 75 x - 9

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

- 126 x^{2} - 75 x - 9 = 0

Factor the expression

More Steps

Evaluate

- 126 x^{2} - 75 x - 9

Rewrite the expression

- 3 \times 42 x^{2} - 3 \times 25 x - 3 \times 3

Factor out - 3 from the expression

- 3 (42 x^{2} + 25 x + 3)

Factor the expression

More Steps

Evaluate

42 x^{2} + 25 x + 3

Rewrite the expression

42 x^{2} + (18 + 7) x + 3

Calculate

42 x^{2} + 18 x + 7 x + 3

Rewrite the expression

6 x \times 7 x + 6 x \times 3 + 7 x + 3

Factor out 6 x from the expression

6 x (7 x + 3) + 7 x + 3

Factor out 7 x + 3 from the expression

(6 x + 1) (7 x + 3)

- 3 (6 x + 1) (7 x + 3)

- 3 (6 x + 1) (7 x + 3) = 0

Divide the terms

(6 x + 1) (7 x + 3) = 0

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

6 x + 1 = 0 7 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

6 x + 1 = 0

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

6 x = 0 - 1

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

6 x = - 1

Divide both sides

\frac{6 x}{6} = \frac{- 1}{6}

Divide the numbers

x = \frac{- 1}{6}

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

x = - \frac{1}{6}

x = - \frac{1}{6} 7 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

7 x + 3 = 0

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

7 x = 0 - 3

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

7 x = - 3

Divide both sides

\frac{7 x}{7} = \frac{- 3}{7}

Divide the numbers

x = \frac{- 3}{7}

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

x = - \frac{3}{7}

x = - \frac{1}{6} x = - \frac{3}{7}

Solution

x_{1} = - \frac{3}{7}, x_{2} = - \frac{1}{6}

Alternative Form

x_{1} = - 0. \dot{4} 2857 \dot{1}, x_{2} = - 0.1 \dot{6}

Show Solution