Solve 9x^2-4+3x^2-7x-6

$$9 x ^ { 2 } - 4 + 3 x ^ { 2 } - 7 x - 6$$

Evaluate

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

Solution Steps

Combine 9x^{2} and 3x^{2} to get 12x^{2}.

$$12x^{2}-4-7x-6$$

Subtract 6 from -4 to get -10.

$$12x^{2}-10-7x$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$12x^{2}-7x-10$$

Factor the expression by grouping. First, the expression needs to be rewritten as 12x^{2}+ax+bx-10. To find a and b, set up a system to be solved.

$$a+b=-7 ab=12\left(-10\right)=-120$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. 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.

$$a=-15 b=8$$

Rewrite 12x^{2}-7x-10 as \left(12x^{2}-15x\right)+\left(8x-10\right).

$$\left(12x^{2}-15x\right)+\left(8x-10\right)$$

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

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

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

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