Solve 6y^2+7y-12y-14

$$6 y ^ { 2 } + 7 y - 12 y - 14$$

Factor

$$\left(y-2\right)\left(6y+7\right)$$

Solution Steps

Multiply and combine like terms.

$$6y^{2}-5y-14$$

Factor the expression by grouping. First, the expression needs to be rewritten as 6y^{2}+ay+by-14. To find a and b, set up a system to be solved.

$$a+b=-5 ab=6\left(-14\right)=-84$$

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 -84.

$$1,-84 2,-42 3,-28 4,-21 6,-14 7,-12$$

Calculate the sum for each pair.

$$1-84=-83 2-42=-40 3-28=-25 4-21=-17 6-14=-8 7-12=-5$$

The solution is the pair that gives sum -5.

$$a=-12 b=7$$

Rewrite 6y^{2}-5y-14 as \left(6y^{2}-12y\right)+\left(7y-14\right).

$$\left(6y^{2}-12y\right)+\left(7y-14\right)$$

Factor out 6y in the first and 7 in the second group.

$$6y\left(y-2\right)+7\left(y-2\right)$$

Factor out common term y-2 by using distributive property.

$$\left(y-2\right)\left(6y+7\right)$$

Evaluate

$$\left(y-2\right)\left(6y+7\right)$$

Solution Steps

Combine 7y and -12y to get -5y.

$$6y^{2}-5y-14$$