Solve 5x^2+5x-6x-6

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

Factor

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

Solution Steps

Multiply and combine like terms.

$$5x^{2}-x-6$$

Factor the expression by grouping. First, the expression needs to be rewritten as 5x^{2}+ax+bx-6. To find a and b, set up a system to be solved.

$$a+b=-1 ab=5\left(-6\right)=-30$$

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 -30.

$$1,-30 2,-15 3,-10 5,-6$$

Calculate the sum for each pair.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

The solution is the pair that gives sum -1.

$$a=-6 b=5$$

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

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

Factor out x in 5x^{2}-6x.

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

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

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

Evaluate

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

Solution Steps

Combine 5x and -6x to get -x.

$$5x^{2}-x-6$$