Solve 6x^2-8x+15x-20

$$6 { x }^{ 2 } -8x+15x-20$$

Factor

$$\left(3x-4\right)\left(2x+5\right)$$

Solution Steps

Multiply and combine like terms.

$$6x^{2}+7x-20$$

Factor the expression by grouping. First, the expression needs to be rewritten as 6x^{2}+ax+bx-20. To find a and b, set up a system to be solved.

$$a+b=7 ab=6\left(-20\right)=-120$$

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 -120.

$$-1,120 -2,60 -3,40 -4,30 -5,24 -6,20 -8,15 -10,12$$

Calculate the sum for each pair.

$$-1+120=119 -2+60=58 -3+40=37 -4+30=26 -5+24=19 -6+20=14 -8+15=7 -10+12=2$$

The solution is the pair that gives sum 7.

$$a=-8 b=15$$

Rewrite 6x^{2}+7x-20 as \left(6x^{2}-8x\right)+\left(15x-20\right).

$$\left(6x^{2}-8x\right)+\left(15x-20\right)$$

Factor out 2x in the first and 5 in the second group.

$$2x\left(3x-4\right)+5\left(3x-4\right)$$

Factor out common term 3x-4 by using distributive property.

$$\left(3x-4\right)\left(2x+5\right)$$

Evaluate

$$\left(3x-4\right)\left(2x+5\right)$$

Solution Steps

Combine -8x and 15x to get 7x.

$$6x^{2}+7x-20$$