Solve 3x^2-20x-63

Question

Factor the expression

(x - 9) (3 x + 7)

Evaluate

3 x^{2} - 20 x - 63

Rewrite the expression

3 x^{2} + (7 - 27) x - 63

Calculate

3 x^{2} + 7 x - 27 x - 63

Rewrite the expression

x \times 3 x + x \times 7 - 9 \times 3 x - 9 \times 7

Factor out x from the expression

x (3 x + 7) - 9 \times 3 x - 9 \times 7

Factor out - 9 from the expression

x (3 x + 7) - 9 (3 x + 7)

Solution

(x - 9) (3 x + 7)

Show Solution

x_{1} = - \frac{7}{3}, x_{2} = 9

Alternative Form

x_{1} = - 2. \dot{3}, x_{2} = 9

Evaluate

3 x^{2} - 20 x - 63

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

3 x^{2} - 20 x - 63 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 20 x - 63

Rewrite the expression

3 x^{2} + (7 - 27) x - 63

Calculate

3 x^{2} + 7 x - 27 x - 63

Rewrite the expression

x \times 3 x + x \times 7 - 9 \times 3 x - 9 \times 7

Factor out x from the expression

x (3 x + 7) - 9 \times 3 x - 9 \times 7

Factor out - 9 from the expression

x (3 x + 7) - 9 (3 x + 7)

Factor out 3 x + 7 from the expression

(x - 9) (3 x + 7)

(x - 9) (3 x + 7) = 0

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

x - 9 = 0 3 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

x - 9 = 0

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

x = 0 + 9

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

x = 9

x = 9 3 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 7 = 0

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

3 x = 0 - 7

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

3 x = - 7

Divide both sides

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

Divide the numbers

x = \frac{- 7}{3}

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

x = - \frac{7}{3}

x = 9 x = - \frac{7}{3}

Solution

x_{1} = - \frac{7}{3}, x_{2} = 9

Alternative Form

x_{1} = - 2. \dot{3}, x_{2} = 9

Show Solution