Solve 6x^2y+7xy-10y

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

Factor

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

Solution Steps

Factor out y.

$$y\left(6x^{2}+7x-10\right)$$

Consider 6x^{2}+7x-10. Factor the expression by grouping. First, the expression needs to be rewritten as 6x^{2}+ax+bx-10. To find a and b, set up a system to be solved.

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

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

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

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

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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