Answer
$x=0$ or $x=-\frac{3}{2}$
Work Step by Step
Step 1: Not needed as there are no fractions.
Step 2: Not needed as there are no parentheses.
Step 3: Not needed as no simplification necessary.
Step 4: The equation $4x(2x+3)=0$ is quadratic.
Step 5: Not needed as the equation is already factored.
Step 6: Not needed as the equation is already factored.
Step 7: $(4x)=0$ or $(2x+3)=0$
Step 8: $x=0$ or $x=-\frac{3}{2}$
Final Step: Checking by substituting the answers in the original equation:
$4x(2x+3)=0$ and $4x(2x+3)=0$
$(4\times0)(2(0)+3)=0$ and $(4\times-\frac{3}{2})(2(-\frac{3}{2})+3)=0$
$0(3)=0$ and $(-6)(0)=0$
$0=0$ and $0=0$
Therefore, the answer checks.