Solve 6x^2-9x+10x-15

$$6 x ^ { 2 } - 9 x + 10 x - 15$$

Factor

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

Solution Steps

Multiply and combine like terms.

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

Factor the expression by grouping. First, the expression needs to be rewritten as 6x^{2}+ax+bx-15. To find a and b, set up a system to be solved.

$$a+b=1 ab=6\left(-15\right)=-90$$

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 -90.

$$-1,90 -2,45 -3,30 -5,18 -6,15 -9,10$$

Calculate the sum for each pair.

$$-1+90=89 -2+45=43 -3+30=27 -5+18=13 -6+15=9 -9+10=1$$

The solution is the pair that gives sum 1.

$$a=-9 b=10$$

Rewrite 6x^{2}+x-15 as \left(6x^{2}-9x\right)+\left(10x-15\right).

$$\left(6x^{2}-9x\right)+\left(10x-15\right)$$

Factor out 3x in the first and 5 in the second group.

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

Factor out common term 2x-3 by using distributive property.

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

Evaluate

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

Solution Steps

Combine -9x and 10x to get x.

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