Solve (3+4z)*(4-10z)=-2z*(3+20z)

$$( 3 + 4 z ) \cdot ( 4 - 10 z ) = - 2 z \cdot ( 3 + 20 z )$$

Solve for z

$$z = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3+4z by 4-10z and combine like terms.

$$12-14z-40z^{2}=-2z\left(3+20z\right)$$

Use the distributive property to multiply -2z by 3+20z.

$$12-14z-40z^{2}=-6z-40z^{2}$$

Add 6z to both sides.

$$12-14z-40z^{2}+6z=-40z^{2}$$

Combine -14z and 6z to get -8z.

$$12-8z-40z^{2}=-40z^{2}$$

Add 40z^{2} to both sides.

$$12-8z-40z^{2}+40z^{2}=0$$

Combine -40z^{2} and 40z^{2} to get 0.

$$12-8z=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-8z=-12$$

Divide both sides by -8.

$$z=\frac{-12}{-8}$$

Reduce the fraction \frac{-12}{-8} to lowest terms by extracting and canceling out -4.

$$z=\frac{3}{2}$$