Solve 2y^2-6y-5y+15

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

Factor

$$\left(y-3\right)\left(2y-5\right)$$

Solution Steps

Multiply and combine like terms.

$$2y^{2}-11y+15$$

Factor the expression by grouping. First, the expression needs to be rewritten as 2y^{2}+ay+by+15. To find a and b, set up a system to be solved.

$$a+b=-11 ab=2\times 15=30$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 30.

$$-1,-30 -2,-15 -3,-10 -5,-6$$

Calculate the sum for each pair.

$$-1-30=-31 -2-15=-17 -3-10=-13 -5-6=-11$$

The solution is the pair that gives sum -11.

$$a=-6 b=-5$$

Rewrite 2y^{2}-11y+15 as \left(2y^{2}-6y\right)+\left(-5y+15\right).

$$\left(2y^{2}-6y\right)+\left(-5y+15\right)$$

Factor out 2y in the first and -5 in the second group.

$$2y\left(y-3\right)-5\left(y-3\right)$$

Factor out common term y-3 by using distributive property.

$$\left(y-3\right)\left(2y-5\right)$$

Evaluate

$$\left(y-3\right)\left(2y-5\right)$$

Solution Steps

Combine -6y and -5y to get -11y.

$$2y^{2}-11y+15$$