Solve 3x ^ 2 - 14x + 8

Question

Factor the expression

(x - 4) (3 x - 2)

Evaluate

3 x^{2} - 14 x + 8

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 4 from the expression

x (3 x - 2) - 4 (3 x - 2)

Solution

(x - 4) (3 x - 2)

Show Solution

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

Alternative Form

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

Evaluate

3 x^{2} - 14 x + 8

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

3 x^{2} - 14 x + 8 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 14 x + 8

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 4 from the expression

x (3 x - 2) - 4 (3 x - 2)

Factor out 3 x - 2 from the expression

(x - 4) (3 x - 2)

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

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

x - 4 = 0 3 x - 2 = 0

Solve the equation for x

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 4 3 x - 2 = 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}

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

Solution

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

Alternative Form

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

Show Solution