Solve -3x^2+22x-24

Question

Factor the expression

- (x - 6) (3 x - 4)

Evaluate

- 3 x^{2} + 22 x - 24

Rewrite the expression

- 3 x^{2} + (4 + 18) x - 24

Calculate

- 3 x^{2} + 4 x + 18 x - 24

Rewrite the expression

- x \times 3 x + x \times 4 + 6 \times 3 x - 6 \times 4

Factor out - x from the expression

- x (3 x - 4) + 6 \times 3 x - 6 \times 4

Factor out 6 from the expression

- x (3 x - 4) + 6 (3 x - 4)

Factor out 3 x - 4 from the expression

(- x + 6) (3 x - 4)

Solution

- (x - 6) (3 x - 4)

Show Solution

x_{1} = \frac{4}{3}, x_{2} = 6

Alternative Form

x_{1} = 1. \dot{3}, x_{2} = 6

Evaluate

- 3 x^{2} + 22 x - 24

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

- 3 x^{2} + 22 x - 24 = 0

Factor the expression

More Steps

Evaluate

- 3 x^{2} + 22 x - 24

Rewrite the expression

- 3 x^{2} + (4 + 18) x - 24

Calculate

- 3 x^{2} + 4 x + 18 x - 24

Rewrite the expression

- x \times 3 x + x \times 4 + 6 \times 3 x - 6 \times 4

Factor out - x from the expression

- x (3 x - 4) + 6 \times 3 x - 6 \times 4

Factor out 6 from the expression

- x (3 x - 4) + 6 (3 x - 4)

Factor out 3 x - 4 from the expression

(- x + 6) (3 x - 4)

(- x + 6) (3 x - 4) = 0

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

- x + 6 = 0 3 x - 4 = 0

Solve the equation for x

More Steps

Evaluate

- x + 6 = 0

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

- x = 0 - 6

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

- x = - 6

Change the signs on both sides of the equation

x = 6

x = 6 3 x - 4 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 4 = 0

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

3 x = 0 + 4

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

3 x = 4

Divide both sides

\frac{3 x}{3} = \frac{4}{3}

Divide the numbers

x = \frac{4}{3}

x = 6 x = \frac{4}{3}

Solution

x_{1} = \frac{4}{3}, x_{2} = 6

Alternative Form

x_{1} = 1. \dot{3}, x_{2} = 6

Show Solution