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

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

Solve for c

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

Solution Steps

Use the distributive property to multiply 3x+5 by 5x+3 and combine like terms.

$$c=15x^{2}+34x+15-2\left(5x+3\right)$$

Use the distributive property to multiply -2 by 5x+3.

$$c=15x^{2}+34x+15-10x-6$$

Combine 34x and -10x to get 24x.

$$c=15x^{2}+24x+15-6$$

Subtract 6 from 15 to get 9.

$$c=15x^{2}+24x+9$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{15c+9}}{15}-\frac{4}{5}$$

$$x=\frac{\sqrt{15c+9}}{15}-\frac{4}{5}$$

Solve for x

$$x=-\frac{\sqrt{15c+9}}{15}-\frac{4}{5}$$

$$x=\frac{\sqrt{15c+9}}{15}-\frac{4}{5}\text{, }c\geq -\frac{3}{5}$$