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

Question

Simplify the expression

6 y^{2} - 13 y - 5

Evaluate

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

3 y \times 2 y

Multiply the numbers

6 y \times y

Multiply the terms

6 y^{2}

6 y^{2} - 3 y \times 5 + 1 \times 2 y - 1 \times 5

Multiply the numbers

6 y^{2} - 15 y + 1 \times 2 y - 1 \times 5

Any expression multiplied by 1 remains the same

6 y^{2} - 15 y + 2 y - 1 \times 5

Any expression multiplied by 1 remains the same

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

Solution

More Steps

Evaluate

- 15 y + 2 y

Collect like terms by calculating the sum or difference of their coefficients

(- 15 + 2) y

Add the numbers

- 13 y

6 y^{2} - 13 y - 5

Show Solution

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

Alternative Form

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

Evaluate

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

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

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

Separate the equation into 2 possible cases

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

Solve the equation

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{1}{3} 2 y - 5 = 0

Solve the equation

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

Solution

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

Alternative Form

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

Show Solution