Solve x^2-6x+9*x^2-x-6

$$x ^ { 2 } - 6 x + 9 \cdot x ^ { 2 } - x - 6$$

Evaluate

$$\left(5x-6\right)\left(2x+1\right)$$

Solution Steps

Combine x^{2} and 9x^{2} to get 10x^{2}.

$$10x^{2}-6x-x-6$$

Combine -6x and -x to get -7x.

$$10x^{2}-7x-6$$

Factor

$$\left(5x-6\right)\left(2x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$10x^{2}-7x-6$$

Factor the expression by grouping. First, the expression needs to be rewritten as 10x^{2}+ax+bx-6. To find a and b, set up a system to be solved.

$$a+b=-7 ab=10\left(-6\right)=-60$$

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 -60.

$$1,-60 2,-30 3,-20 4,-15 5,-12 6,-10$$

Calculate the sum for each pair.

$$1-60=-59 2-30=-28 3-20=-17 4-15=-11 5-12=-7 6-10=-4$$

The solution is the pair that gives sum -7.

$$a=-12 b=5$$

Rewrite 10x^{2}-7x-6 as \left(10x^{2}-12x\right)+\left(5x-6\right).

$$\left(10x^{2}-12x\right)+\left(5x-6\right)$$

Factor out 2x in 10x^{2}-12x.

$$2x\left(5x-6\right)+5x-6$$

Factor out common term 5x-6 by using distributive property.

$$\left(5x-6\right)\left(2x+1\right)$$