\( \leftarrow \quad \) Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying \( x \)-intercepts. \[ 4 x^{2}+16 x=0 \]

Solve the equation \( 4x^2+16x=0 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(4x^{2}+16x=0\) - step1: Factor the expression: \(4x\left(x+4\right)=0\) - step2: Separate into possible cases: \(\begin{align}&4x=0\\&x+4=0\end{align}\) - step3: Solve the equation: \(\begin{align}&x=0\\&x=-4\end{align}\) - step4: Rewrite: \(x_{1}=-4,x_{2}=0\) The solutions to the quadratic equation \(4x^2 + 16x = 0\) are \(x = -4\) and \(x = 0\). To check these solutions, we can substitute them back into the original equation: 1. For \(x = -4\): \[4(-4)^2 + 16(-4) = 4(16) - 64 = 64 - 64 = 0\] 2. For \(x = 0\): \[4(0)^2 + 16(0) = 0 + 0 = 0\] Both solutions satisfy the original equation, confirming that the solutions are \(x = -4\) and \(x = 0\).