To solve the equation 2x(x+3) = x -4, we need to first simplify the left-hand side of the equation by multiplying out the brackets:
2x(x+3) = 2x^2 + 6x
Now, we can rewrite the equation as:
2x^2 + 6x = x - 4
To solve for x, we need to bring all the terms to one side of the equation. Let's start by subtracting x and adding 4 to both sides:
2x^2 + 5x + 4 = 0
Now, we can factor this quadratic equation. To do this, we need to find two numbers that multiply to give 8 and add to give 5. These numbers are 1 and 4. So, we can rewrite the equation as:
(2x + 1)(x + 4) = 0
This means that either 2x + 1 = 0 or x + 4 = 0.
Solving for 2x + 1 = 0, we get:
2x + 1 = 0
2x = -1
x = -1/2
Solving for x + 4 = 0, we get:
x + 4 = 0
x = -4
Therefore, the solutions to the equation 2x(x+3) = x -4 are x = -1/2 and x = -4