Solve 6m^2-3m+2-m^2-(-4m)-6

$$6 m ^ { 2 } - 3 m + 2 - m ^ { 2 } - ( - 4 m ) - 6$$

Evaluate

$$\left(5m-4\right)\left(m+1\right)$$

Solution Steps

Combine 6m^{2} and -m^{2} to get 5m^{2}.

$$5m^{2}-3m+2-\left(-4m\right)-6$$

The opposite of -4m is 4m.

$$5m^{2}-3m+2+4m-6$$

Combine -3m and 4m to get m.

$$5m^{2}+m+2-6$$

Subtract 6 from 2 to get -4.

$$5m^{2}+m-4$$

Factor

$$\left(5m-4\right)\left(m+1\right)$$

Solution Steps

Multiply and combine like terms.

$$5m^{2}+m-4$$

Factor the expression by grouping. First, the expression needs to be rewritten as 5m^{2}+am+bm-4. To find a and b, set up a system to be solved.

$$a+b=1 ab=5\left(-4\right)=-20$$

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 -20.

$$-1,20 -2,10 -4,5$$

Calculate the sum for each pair.

$$-1+20=19 -2+10=8 -4+5=1$$

The solution is the pair that gives sum 1.

$$a=-4 b=5$$

Rewrite 5m^{2}+m-4 as \left(5m^{2}-4m\right)+\left(5m-4\right).

$$\left(5m^{2}-4m\right)+\left(5m-4\right)$$

Factor out m in 5m^{2}-4m.

$$m\left(5m-4\right)+5m-4$$

Factor out common term 5m-4 by using distributive property.

$$\left(5m-4\right)\left(m+1\right)$$