Solve 6y^2-13y-5 - ScanMath

Question

Factor the expression

(2 y - 5) (3 y + 1)

Evaluate

6 y^{2} - 13 y - 5

Rewrite the expression

6 y^{2} + (2 - 15) y - 5

Calculate

6 y^{2} + 2 y - 15 y - 5

Rewrite the expression

2 y \times 3 y + 2 y - 5 \times 3 y - 5

Factor out 2 y from the expression

2 y (3 y + 1) - 5 \times 3 y - 5

Factor out - 5 from the expression

2 y (3 y + 1) - 5 (3 y + 1)

Solution

(2 y - 5) (3 y + 1)

Show Solution

y_{1} = - \frac{1}{3}, y_{2} = \frac{5}{2}

Alternative Form

y_{1} = - 0. \dot{3}, y_{2} = 2.5

Evaluate

6 y^{2} - 13 y - 5

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

6 y^{2} - 13 y - 5 = 0

Factor the expression

More Steps

Evaluate

6 y^{2} - 13 y - 5

Rewrite the expression

6 y^{2} + (2 - 15) y - 5

Calculate

6 y^{2} + 2 y - 15 y - 5

Rewrite the expression

2 y \times 3 y + 2 y - 5 \times 3 y - 5

Factor out 2 y from the expression

2 y (3 y + 1) - 5 \times 3 y - 5

Factor out - 5 from the expression

2 y (3 y + 1) - 5 (3 y + 1)

Factor out 3 y + 1 from the expression

(2 y - 5) (3 y + 1)

(2 y - 5) (3 y + 1) = 0

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

2 y - 5 = 0 3 y + 1 = 0

Solve the equation for y

More Steps

Evaluate

2 y - 5 = 0

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

2 y = 0 + 5

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

2 y = 5

Divide both sides

\frac{2 y}{2} = \frac{5}{2}

Divide the numbers

y = \frac{5}{2}

y = \frac{5}{2} 3 y + 1 = 0

Solve the equation for y

More Steps

Evaluate

3 y + 1 = 0

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

3 y = 0 - 1

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

3 y = - 1

Divide both sides

\frac{3 y}{3} = \frac{- 1}{3}

Divide the numbers

y = \frac{- 1}{3}

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

y = - \frac{1}{3}

y = \frac{5}{2} y = - \frac{1}{3}

Solution

y_{1} = - \frac{1}{3}, y_{2} = \frac{5}{2}

Alternative Form

y_{1} = - 0. \dot{3}, y_{2} = 2.5

Show Solution