Solve -4xyz^2-3xyz^2+3x^2+3/2x^2-1/2xy{z}^2

$$-4xy { z }^{ 2 } -3xy { z }^{ 2 } +3 { x }^{ 2 } + \frac{ 3 }{ 2 } { x }^{ 2 } - \frac{ 1 }{ 2 } xy { z }^{ 2 }$$

Factor

$$\frac{3x\left(3x-5yz^{2}\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{-8xyz^{2}-6xyz^{2}+6x^{2}+3x^{2}-xyz^{2}}{2}$$

Consider -8xyz^{2}-6xyz^{2}+6x^{2}+3x^{2}-xyz^{2}. Factor out x.

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

Consider -8yz^{2}-6yz^{2}+6x+3x-yz^{2}. Multiply and combine like terms.

$$9x-15yz^{2}$$

Consider 9x-15yz^{2}. Factor out 3.

$$3\left(3x-5yz^{2}\right)$$

Rewrite the complete factored expression.

$$\frac{3x\left(3x-5yz^{2}\right)}{2}$$

Evaluate

$$\frac{3x\left(3x-5yz^{2}\right)}{2}$$