## Solving a Quadratic Equation in Standard Form

This article will guide you through the process of solving the equation **(x+5)(2x-3) = 2(x+1)** and writing it in standard form.

### Step 1: Expand the equation

Begin by expanding both sides of the equation to remove the parentheses:

**Left side:**(x+5)(2x-3) = 2x² - 3x + 10x - 15 = 2x² + 7x - 15**Right side:**2(x+1) = 2x + 2

This simplifies the equation to: 2x² + 7x - 15 = 2x + 2

### Step 2: Move all terms to one side

To put the equation in standard form, we need all terms on one side, setting the equation equal to zero:

2x² + 7x - 15 - 2x - 2 = 0

### Step 3: Combine like terms

Combine the x terms and the constant terms:

2x² + 5x - 17 = 0

### Step 4: Standard Form

The equation is now in standard quadratic form: **ax² + bx + c = 0**, where a = 2, b = 5, and c = -17.

Therefore, the standard form of the equation **(x+5)(2x-3) = 2(x+1)** is **2x² + 5x - 17 = 0**.

### Further Steps

From here, you can solve for x using various methods, such as:

**Factoring:**If the equation can be factored, you can find the values of x that make the equation true.**Quadratic Formula:**This formula can be used to find the solutions for any quadratic equation.**Completing the Square:**This method involves manipulating the equation to form a perfect square trinomial.