Solve 32c^2+72c-12c-27

$$32 c ^ { 2 } + 72 c - 12 c - 27$$

Factor

$$\left(8c-3\right)\left(4c+9\right)$$

Solution Steps

Multiply and combine like terms.

$$32c^{2}+60c-27$$

Factor the expression by grouping. First, the expression needs to be rewritten as 32c^{2}+ac+bc-27. To find a and b, set up a system to be solved.

$$a+b=60 ab=32\left(-27\right)=-864$$

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 -864.

$$-1,864 -2,432 -3,288 -4,216 -6,144 -8,108 -9,96 -12,72 -16,54 -18,48 -24,36 -27,32$$

Calculate the sum for each pair.

$$-1+864=863 -2+432=430 -3+288=285 -4+216=212 -6+144=138 -8+108=100 -9+96=87 -12+72=60 -16+54=38 -18+48=30 -24+36=12 -27+32=5$$

The solution is the pair that gives sum 60.

$$a=-12 b=72$$

Rewrite 32c^{2}+60c-27 as \left(32c^{2}-12c\right)+\left(72c-27\right).

$$\left(32c^{2}-12c\right)+\left(72c-27\right)$$

Factor out 4c in the first and 9 in the second group.

$$4c\left(8c-3\right)+9\left(8c-3\right)$$

Factor out common term 8c-3 by using distributive property.

$$\left(8c-3\right)\left(4c+9\right)$$

Evaluate

$$\left(8c-3\right)\left(4c+9\right)$$

Solution Steps

Combine 72c and -12c to get 60c.

$$32c^{2}+60c-27$$