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

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

Factor

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

Solution Steps

Multiply and combine like terms.

$$-2x^{2}-4x+6$$

Factor out 2.

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

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

$$a+b=-2 ab=-3=-3$$

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. The only such pair is the system solution.

$$a=1 b=-3$$

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

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

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

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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

Solution Steps

Combine x and -5x to get -4x.

$$-4x-2x^{2}+6$$