Solve 8x^2-6x+12x-9

$$8 { x }^{ 2 } -6x+12x-9$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$8x^{2}+6x-9$$

Factor the expression by grouping. First, the expression needs to be rewritten as 8x^{2}+ax+bx-9. To find a and b, set up a system to be solved.

$$a+b=6 ab=8\left(-9\right)=-72$$

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 -72.

$$-1,72 -2,36 -3,24 -4,18 -6,12 -8,9$$

Calculate the sum for each pair.

$$-1+72=71 -2+36=34 -3+24=21 -4+18=14 -6+12=6 -8+9=1$$

The solution is the pair that gives sum 6.

$$a=-6 b=12$$

Rewrite 8x^{2}+6x-9 as \left(8x^{2}-6x\right)+\left(12x-9\right).

$$\left(8x^{2}-6x\right)+\left(12x-9\right)$$

Factor out 2x in the first and 3 in the second group.

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

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

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

Evaluate

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

Solution Steps

Combine -6x and 12x to get 6x.

$$8x^{2}+6x-9$$