Solve 600-30x-40x+2x^2

$$600 - 30 x - 40 x + 2 x ^ { 2 }$$

Factor

$$2\left(x-20\right)\left(x-15\right)$$

Solution Steps

Factor out 2.

$$2\left(300-15x-20x+x^{2}\right)$$

Consider 300-15x-20x+x^{2}. Multiply and combine like terms.

$$x^{2}-35x+300$$

Consider x^{2}-35x+300. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+300. To find a and b, set up a system to be solved.

$$a+b=-35 ab=1\times 300=300$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 300.

$$-1,-300 -2,-150 -3,-100 -4,-75 -5,-60 -6,-50 -10,-30 -12,-25 -15,-20$$

Calculate the sum for each pair.

$$-1-300=-301 -2-150=-152 -3-100=-103 -4-75=-79 -5-60=-65 -6-50=-56 -10-30=-40 -12-25=-37 -15-20=-35$$

The solution is the pair that gives sum -35.

$$a=-20 b=-15$$

Rewrite x^{2}-35x+300 as \left(x^{2}-20x\right)+\left(-15x+300\right).

$$\left(x^{2}-20x\right)+\left(-15x+300\right)$$

Factor out x in the first and -15 in the second group.

$$x\left(x-20\right)-15\left(x-20\right)$$

Factor out common term x-20 by using distributive property.

$$\left(x-20\right)\left(x-15\right)$$

Rewrite the complete factored expression.

$$2\left(x-20\right)\left(x-15\right)$$

Evaluate

$$2\left(x-20\right)\left(x-15\right)$$

Solution Steps

Combine -30x and -40x to get -70x.

$$600-70x+2x^{2}$$