Solve each of the following equatins :
`5x^(2)+4x=0`

Answer

To solve the quadratic equation \( 5x^2 + 4x = 0 \), we can follow these steps:

### Step 1: Factor the equation
We start with the equation:
\[ 5x^2 + 4x = 0 \]
We can factor out \( x \) from the left-hand side:
\[ x(5x + 4) = 0 \]

### Step 2: Set each factor to zero
Now, we set each factor equal to zero:
1. \( x = 0 \)
2. \( 5x + 4 = 0 \)

### Step 3: Solve for \( x \) from the second factor
For the second factor, we solve for \( x \):
\[ 5x + 4 = 0 \]
Subtract 4 from both sides:
\[ 5x = -4 \]
Now, divide both sides by 5:
\[ x = -\frac{4}{5} \]

### Step 4: Write the final solutions
The solutions to the equation \( 5x^2 + 4x = 0 \) are:
\[ x = 0 \quad \text{or} \quad x = -\frac{4}{5} \]

### Final Answer:
The solutions are:
\[ x = 0 \quad \text{and} \quad x = -\frac{4}{5} \]

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