Solve 3x^2-14x+15

Question

Factor the expression

(x - 3) (3 x - 5)

Evaluate

3 x^{2} - 14 x + 15

Rewrite the expression

3 x^{2} + (- 5 - 9) x + 15

Calculate

3 x^{2} - 5 x - 9 x + 15

Rewrite the expression

x \times 3 x - x \times 5 - 3 \times 3 x + 3 \times 5

Factor out x from the expression

x (3 x - 5) - 3 \times 3 x + 3 \times 5

Factor out - 3 from the expression

x (3 x - 5) - 3 (3 x - 5)

Solution

(x - 3) (3 x - 5)

Show Solution

x_{1} = \frac{5}{3}, x_{2} = 3

Alternative Form

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

Evaluate

3 x^{2} - 14 x + 15

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

3 x^{2} - 14 x + 15 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 14 x + 15

Rewrite the expression

3 x^{2} + (- 5 - 9) x + 15

Calculate

3 x^{2} - 5 x - 9 x + 15

Rewrite the expression

x \times 3 x - x \times 5 - 3 \times 3 x + 3 \times 5

Factor out x from the expression

x (3 x - 5) - 3 \times 3 x + 3 \times 5

Factor out - 3 from the expression

x (3 x - 5) - 3 (3 x - 5)

Factor out 3 x - 5 from the expression

(x - 3) (3 x - 5)

(x - 3) (3 x - 5) = 0

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

x - 3 = 0 3 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 3 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 5 = 0

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

3 x = 0 + 5

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

3 x = 5

Divide both sides

\frac{3 x}{3} = \frac{5}{3}

Divide the numbers

x = \frac{5}{3}

x = 3 x = \frac{5}{3}

Solution

x_{1} = \frac{5}{3}, x_{2} = 3

Alternative Form

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

Show Solution