Solve 14x+6x^2-6-5x

$$14 x + 6 x ^ { 2 } - 6 - 5 x$$

Factor

$$3\left(2x-1\right)\left(x+2\right)$$

Solution Steps

Multiply and combine like terms.

$$6x^{2}+9x-6$$

Factor out 3.

$$3\left(2x^{2}+3x-2\right)$$

Consider 2x^{2}+3x-2. Factor the expression by grouping. First, the expression needs to be rewritten as 2x^{2}+ax+bx-2. To find a and b, set up a system to be solved.

$$a+b=3 ab=2\left(-2\right)=-4$$

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 -4.

$$-1,4 -2,2$$

Calculate the sum for each pair.

$$-1+4=3 -2+2=0$$

The solution is the pair that gives sum 3.

$$a=-1 b=4$$

Rewrite 2x^{2}+3x-2 as \left(2x^{2}-x\right)+\left(4x-2\right).

$$\left(2x^{2}-x\right)+\left(4x-2\right)$$

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

$$x\left(2x-1\right)+2\left(2x-1\right)$$

Factor out common term 2x-1 by using distributive property.

$$\left(2x-1\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$3\left(2x-1\right)\left(x+2\right)$$

Evaluate

$$3\left(2x-1\right)\left(x+2\right)$$

Solution Steps

Combine 14x and -5x to get 9x.

$$9x+6x^{2}-6$$