Solve C=(7-2x)(4+3x)+(2-7x)(3x+4)

$$C = ( 7 - 2 x ) ( 4 + 3 x ) + ( 2 - 7 x ) ( 3 x + 4 )$$

Solve for C

$$C=-9\left(x-1\right)\left(3x+4\right)$$

Solution Steps

Use the distributive property to multiply 7-2x by 4+3x and combine like terms.

$$C=28+13x-6x^{2}+\left(2-7x\right)\left(3x+4\right)$$

Use the distributive property to multiply 2-7x by 3x+4 and combine like terms.

$$C=28+13x-6x^{2}-22x+8-21x^{2}$$

Combine 13x and -22x to get -9x.

$$C=28-9x-6x^{2}+8-21x^{2}$$

Add 28 and 8 to get 36.

$$C=36-9x-6x^{2}-21x^{2}$$

Combine -6x^{2} and -21x^{2} to get -27x^{2}.

$$C=36-9x-27x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{441-12C}}{18}-\frac{1}{6}$$

$$x=-\frac{\sqrt{441-12C}}{18}-\frac{1}{6}$$

Solve for x

$$x=\frac{\sqrt{441-12C}}{18}-\frac{1}{6}$$

$$x=-\frac{\sqrt{441-12C}}{18}-\frac{1}{6}\text{, }C\leq \frac{147}{4}$$