Solve C=-2(x+1)(4-x)+3x(2+3x)

$$C = - 2 ( x + 1 ) ( 4 - x ) + 3 x ( 2 + 3 x )$$

Solve for C

$$C=11x^{2}-8$$

Solution Steps

Use the distributive property to multiply -2 by x+1.

$$C=\left(-2x-2\right)\left(4-x\right)+3x\left(2+3x\right)$$

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

$$C=-6x+2x^{2}-8+3x\left(2+3x\right)$$

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

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

Combine -6x and 6x to get 0.

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

Combine 2x^{2} and 9x^{2} to get 11x^{2}.

$$C=11x^{2}-8$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{11\left(C+8\right)}}{11}$$

$$x=\frac{\sqrt{11\left(C+8\right)}}{11}$$

Solve for x

$$x=\frac{\sqrt{11\left(C+8\right)}}{11}$$

$$x=-\frac{\sqrt{11\left(C+8\right)}}{11}\text{, }C\geq -8$$