Question

( x-3 ).( 2x-3 ) = 0

Answer 1

`x=3, x=(3)/(2)`

Explanation:

`\left(x-3\right)\left(2x-3\right)=0`

The zero product theorem will be used here to solve this non-linear problem.

means that in the original equation, each variable component must be set to zero.

`\begin{cases} x-3=0\\2x -3=0\end{cases}`

To solve this linear equation, we need to group all of the variable terms on one side of the equation and all of the constant terms on the other.

so, -3 will be moved to the right side

Notice that when a term moves from one side of the equation to the other, it changes sign.

`\begin{cases} (x-3)+3=3\\(2x-3)+3=3 \end{cases}`

`x\left \{ 3,(3)/(2) \}`

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Answer 2

Explanation:

Assuming you want to find x, we can set two equations:

x-3=0

2x-3=0

This is so that we can individually find x within the two paranthesis and not have to do more work. It helps for standardized tests.

solve for x on both sides, and you get 3 and 1.5