Solve 6x-5x^2-13x+12

$$6 x - 5 x ^ { 2 } - 13 x + 12$$

Factor

$$\left(1-x\right)\left(5x+12\right)$$

Solution Steps

Multiply and combine like terms.

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

Factor the expression by grouping. First, the expression needs to be rewritten as -5x^{2}+ax+bx+12. To find a and b, set up a system to be solved.

$$a+b=-7 ab=-5\times 12=-60$$

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.

$$a=5 b=-12$$

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

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

Factor out 5x in the first and 12 in the second group.

$$5x\left(-x+1\right)+12\left(-x+1\right)$$

Factor out common term -x+1 by using distributive property.

$$\left(-x+1\right)\left(5x+12\right)$$

Evaluate

$$\left(1-x\right)\left(5x+12\right)$$

Solution Steps

Combine 6x and -13x to get -7x.

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