Solve 10x^2-6+5x-3x^2-12

$$10 x ^ { 2 } - 6 + 5 x - 3 x ^ { 2 } - 12$$

Evaluate

$$\left(7x-9\right)\left(x+2\right)$$

Solution Steps

Combine 10x^{2} and -3x^{2} to get 7x^{2}.

$$7x^{2}-6+5x-12$$

Subtract 12 from -6 to get -18.

$$7x^{2}-18+5x$$

Factor

$$\left(7x-9\right)\left(x+2\right)$$

Solution Steps

Multiply and combine like terms.

$$7x^{2}+5x-18$$

Factor the expression by grouping. First, the expression needs to be rewritten as 7x^{2}+ax+bx-18. To find a and b, set up a system to be solved.

$$a+b=5 ab=7\left(-18\right)=-126$$

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 -126.

$$-1,126 -2,63 -3,42 -6,21 -7,18 -9,14$$

Calculate the sum for each pair.

$$-1+126=125 -2+63=61 -3+42=39 -6+21=15 -7+18=11 -9+14=5$$

The solution is the pair that gives sum 5.

$$a=-9 b=14$$

Rewrite 7x^{2}+5x-18 as \left(7x^{2}-9x\right)+\left(14x-18\right).

$$\left(7x^{2}-9x\right)+\left(14x-18\right)$$

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

$$x\left(7x-9\right)+2\left(7x-9\right)$$

Factor out common term 7x-9 by using distributive property.

$$\left(7x-9\right)\left(x+2\right)$$