Solve 15x^2+20x-12x-16

$$15 x ^ { 2 } + 20 x - 12 x - 16$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$15x^{2}+8x-16$$

Factor the expression by grouping. First, the expression needs to be rewritten as 15x^{2}+ax+bx-16. To find a and b, set up a system to be solved.

$$a+b=8 ab=15\left(-16\right)=-240$$

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 -240.

$$-1,240 -2,120 -3,80 -4,60 -5,48 -6,40 -8,30 -10,24 -12,20 -15,16$$

Calculate the sum for each pair.

$$-1+240=239 -2+120=118 -3+80=77 -4+60=56 -5+48=43 -6+40=34 -8+30=22 -10+24=14 -12+20=8 -15+16=1$$

The solution is the pair that gives sum 8.

$$a=-12 b=20$$

Rewrite 15x^{2}+8x-16 as \left(15x^{2}-12x\right)+\left(20x-16\right).

$$\left(15x^{2}-12x\right)+\left(20x-16\right)$$

Factor out 3x in the first and 4 in the second group.

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

Factor out common term 5x-4 by using distributive property.

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

Evaluate

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

Solution Steps

Combine 20x and -12x to get 8x.

$$15x^{2}+8x-16$$