Step 1: Expand the Equation
To start solving the equation (x + 3)(3x + 87) = 360, we need to expand the left side:
- Distribute (x + 3) with (3x + 87):
- x * 3x = 3x²
- x * 87 = 87x
- 3 * 3x = 9x
- 3 * 87 = 261
Combining these gives:
- 3x² + 96x + 261 = 360
Step 2: Rearrange the Equation
Next, we want to set the equation to zero:
- Subtract 360 from both sides:
- 3x² + 96x + 261 - 360 = 0
- This simplifies to: 3x² + 96x - 99 = 0
Step 3: Simplify the Equation
We can simplify by dividing the entire equation by 3:
- x² + 32x - 33 = 0
Step 4: Factor the Quadratic Equation
Now, we need to factor x² + 32x - 33:
- Look for two numbers that multiply to -33 and add to 32.
- The numbers are 33 and -1.
Thus, we can factor it as:
- (x + 33)(x - 1) = 0
Step 5: Solve for x
Now, set each factor to zero:
- x + 33 = 0 → x = -33
- x - 1 = 0 → x = 1
Conclusion
The solutions to the equation (x + 3)(3x + 87) = 360 are:
- x = -33
- x = 1
These values can be verified by substituting back into the original equation.