Solve c=6(x+1)(3x-2)-2(2-5x)(x+1)

$$c = 6 ( x + 1 ) ( 3 x - 2 ) - 2 ( 2 - 5 x ) ( x + 1 )$$

Solve for c

$$c=4\left(7x-4\right)\left(x+1\right)$$

Solution Steps

Use the distributive property to multiply 6 by x+1.

$$c=\left(6x+6\right)\left(3x-2\right)-2\left(2-5x\right)\left(x+1\right)$$

Use the distributive property to multiply 6x+6 by 3x-2 and combine like terms.

$$c=18x^{2}+6x-12-2\left(2-5x\right)\left(x+1\right)$$

Use the distributive property to multiply -2 by 2-5x.

$$c=18x^{2}+6x-12+\left(-4+10x\right)\left(x+1\right)$$

Use the distributive property to multiply -4+10x by x+1 and combine like terms.

$$c=18x^{2}+6x-12+6x-4+10x^{2}$$

Combine 6x and 6x to get 12x.

$$c=18x^{2}+12x-12-4+10x^{2}$$

Subtract 4 from -12 to get -16.

$$c=18x^{2}+12x-16+10x^{2}$$

Combine 18x^{2} and 10x^{2} to get 28x^{2}.

$$c=28x^{2}+12x-16$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{7c+121}-3}{14}$$

$$x=\frac{\sqrt{7c+121}-3}{14}$$

Solve for x

$$x=\frac{-\sqrt{7c+121}-3}{14}$$

$$x=\frac{\sqrt{7c+121}-3}{14}\text{, }c\geq -\frac{121}{7}$$