Solve -7x^2+2x-5x^2+4

$$- 7 x ^ { 2 } + 2 x - 5 x ^ { 2 } + 4$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$-12x^{2}+2x+4$$

Factor out 2.

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

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

$$a+b=1 ab=-6\times 2=-12$$

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 -12.

$$-1,12 -2,6 -3,4$$

Calculate the sum for each pair.

$$-1+12=11 -2+6=4 -3+4=1$$

The solution is the pair that gives sum 1.

$$a=4 b=-3$$

Rewrite -6x^{2}+x+2 as \left(-6x^{2}+4x\right)+\left(-3x+2\right).

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

Factor out 2x in -6x^{2}+4x.

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

Factor out common term -3x+2 by using distributive property.

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

Rewrite the complete factored expression.

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

Evaluate

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

Solution Steps

Combine -7x^{2} and -5x^{2} to get -12x^{2}.

$$-12x^{2}+2x+4$$