Solve c=(3x-4/3)(5x+1)-(5/3x+4

$$c = ( 3 x - \frac { 4 } { 3 } ) ( 5 x + 1 ) - ( \frac { 5 } { 3 } x + 4$$

Solve for c

$$c=15x^{2}-\frac{16x}{3}-\frac{16}{3}$$

Solution Steps

Use the distributive property to multiply 3x-\frac{4}{3} by 5x+1 and combine like terms.

$$c=15x^{2}-\frac{11}{3}x-\frac{4}{3}-\left(\frac{5}{3}x+4\right)$$

To find the opposite of \frac{5}{3}x+4, find the opposite of each term.

$$c=15x^{2}-\frac{11}{3}x-\frac{4}{3}-\frac{5}{3}x-4$$

Combine -\frac{11}{3}x and -\frac{5}{3}x to get -\frac{16}{3}x.

$$c=15x^{2}-\frac{16}{3}x-\frac{4}{3}-4$$

Subtract 4 from -\frac{4}{3} to get -\frac{16}{3}.

$$c=15x^{2}-\frac{16}{3}x-\frac{16}{3}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{135c+784}+8}{45}$$

$$x=\frac{\sqrt{135c+784}+8}{45}$$

Solve for x

$$x=\frac{-\sqrt{135c+784}+8}{45}$$

$$x=\frac{\sqrt{135c+784}+8}{45}\text{, }c\geq -\frac{784}{135}$$