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

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

Factor

$$\left(2x-5\right)\left(x+3\right)$$

Solution Steps

Multiply and combine like terms.

$$2x^{2}+x-15$$

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

$$a+b=1 ab=2\left(-15\right)=-30$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -30.

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

Calculate the sum for each pair.

$$-1+30=29 -2+15=13 -3+10=7 -5+6=1$$

The solution is the pair that gives sum 1.

$$a=-5 b=6$$

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

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

Factor out x in the first and 3 in the second group.

$$x\left(2x-5\right)+3\left(2x-5\right)$$

Factor out common term 2x-5 by using distributive property.

$$\left(2x-5\right)\left(x+3\right)$$

Evaluate

$$\left(2x-5\right)\left(x+3\right)$$

Solution Steps

Combine 6x and -5x to get x.

$$2x^{2}+x-15$$