Solve 6x^2+14x-15x-35

$$6 { x }^{ 2 } +14x-15x-35$$

Factor

$$\left(2x-5\right)\left(3x+7\right)$$

Solution Steps

Multiply and combine like terms.

$$6x^{2}-x-35$$

Factor the expression by grouping. First, the expression needs to be rewritten as 6x^{2}+ax+bx-35. To find a and b, set up a system to be solved.

$$a+b=-1 ab=6\left(-35\right)=-210$$

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 -210.

$$1,-210 2,-105 3,-70 5,-42 6,-35 7,-30 10,-21 14,-15$$

Calculate the sum for each pair.

$$1-210=-209 2-105=-103 3-70=-67 5-42=-37 6-35=-29 7-30=-23 10-21=-11 14-15=-1$$

The solution is the pair that gives sum -1.

$$a=-15 b=14$$

Rewrite 6x^{2}-x-35 as \left(6x^{2}-15x\right)+\left(14x-35\right).

$$\left(6x^{2}-15x\right)+\left(14x-35\right)$$

Factor out 3x in the first and 7 in the second group.

$$3x\left(2x-5\right)+7\left(2x-5\right)$$

Factor out common term 2x-5 by using distributive property.

$$\left(2x-5\right)\left(3x+7\right)$$

Evaluate

$$\left(2x-5\right)\left(3x+7\right)$$

Solution Steps

Combine 14x and -15x to get -x.

$$6x^{2}-x-35$$