Solve c=(2x+2)(5x-5)+(2x+3)(3x-7)

$$c = ( 2 x + 2 ) ( 5 x - 5 ) + ( 2 x + 3 ) ( 3 x - 7 )$$

Solve for c

$$c=16x^{2}-5x-31$$

Solution Steps

Use the distributive property to multiply 2x+2 by 5x-5 and combine like terms.

$$c=10x^{2}-10+\left(2x+3\right)\left(3x-7\right)$$

Use the distributive property to multiply 2x+3 by 3x-7 and combine like terms.

$$c=10x^{2}-10+6x^{2}-5x-21$$

Combine 10x^{2} and 6x^{2} to get 16x^{2}.

$$c=16x^{2}-10-5x-21$$

Subtract 21 from -10 to get -31.

$$c=16x^{2}-31-5x$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{64c+2009}+5}{32}$$

$$x=\frac{\sqrt{64c+2009}+5}{32}$$

Solve for x

$$x=\frac{-\sqrt{64c+2009}+5}{32}$$

$$x=\frac{\sqrt{64c+2009}+5}{32}\text{, }c\geq -\frac{2009}{64}$$