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

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

Factor

$$\left(3a-4\right)\left(2x^{2}+3\right)$$

Solution Steps

Do the grouping 6ax^{2}+9a-8x^{2}-12=\left(6ax^{2}+9a\right)+\left(-8x^{2}-12\right), and factor out 3a in the first and -4 in the second group.

$$3a\left(2x^{2}+3\right)-4\left(2x^{2}+3\right)$$

Factor out common term 2x^{2}+3 by using distributive property. Polynomial 2x^{2}+3 is not factored since it does not have any rational roots.

$$\left(2x^{2}+3\right)\left(3a-4\right)$$

Evaluate

$$\left(3a-4\right)\left(2x^{2}+3\right)$$