Solve 6y-3y^2+8-4y

$$6y-3 { y }^{ 2 } +8-4y$$

Factor

$$\left(2-y\right)\left(3y+4\right)$$

Solution Steps

Multiply and combine like terms.

$$-3y^{2}+2y+8$$

Factor the expression by grouping. First, the expression needs to be rewritten as -3y^{2}+ay+by+8. To find a and b, set up a system to be solved.

$$a+b=2 ab=-3\times 8=-24$$

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 -24.

$$-1,24 -2,12 -3,8 -4,6$$

Calculate the sum for each pair.

$$-1+24=23 -2+12=10 -3+8=5 -4+6=2$$

The solution is the pair that gives sum 2.

$$a=6 b=-4$$

Rewrite -3y^{2}+2y+8 as \left(-3y^{2}+6y\right)+\left(-4y+8\right).

$$\left(-3y^{2}+6y\right)+\left(-4y+8\right)$$

Factor out 3y in the first and 4 in the second group.

$$3y\left(-y+2\right)+4\left(-y+2\right)$$

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

$$\left(-y+2\right)\left(3y+4\right)$$

Evaluate

$$\left(2-y\right)\left(3y+4\right)$$

Solution Steps

Combine 6y and -4y to get 2y.

$$2y-3y^{2}+8$$