Solve [3x-11*(2x+z)-(x+1)*16x-5]=7

$$[ 3 x - 11 \cdot ( 2 x + z ) - ( x + 1 ) \cdot 16 x - 5 ] = 7$$

Solve for z

$$z=\frac{-16x^{2}-35x-12}{11}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -11 by 2x+z.

$$3x-22x-11z-\left(x+1\right)\times 16x-5=7$$

Combine 3x and -22x to get -19x.

$$-19x-11z-\left(x+1\right)\times 16x-5=7$$

Use the distributive property to multiply x+1 by 16.

$$-19x-11z-\left(16x+16\right)x-5=7$$

Use the distributive property to multiply 16x+16 by x.

$$-19x-11z-\left(16x^{2}+16x\right)-5=7$$

To find the opposite of 16x^{2}+16x, find the opposite of each term.

$$-19x-11z-16x^{2}-16x-5=7$$

Combine -19x and -16x to get -35x.

$$-35x-11z-16x^{2}-5=7$$

Add 35x to both sides.

$$-11z-16x^{2}-5=7+35x$$

Add 16x^{2} to both sides.

$$-11z-5=7+35x+16x^{2}$$

Add 5 to both sides.

$$-11z=7+35x+16x^{2}+5$$

Add 7 and 5 to get 12.

$$-11z=12+35x+16x^{2}$$

The equation is in standard form.

$$-11z=16x^{2}+35x+12$$

Divide both sides by -11.

$$\frac{-11z}{-11}=\frac{16x^{2}+35x+12}{-11}$$

Dividing by -11 undoes the multiplication by -11.

$$z=\frac{16x^{2}+35x+12}{-11}$$

Divide 12+35x+16x^{2} by -11.

$$z=\frac{-16x^{2}-35x-12}{11}$$

Solve for x

$$x=\frac{-\sqrt{457-704z}-35}{32}$$

$$x=\frac{\sqrt{457-704z}-35}{32}\text{, }z\leq \frac{457}{704}$$