Answer:
Sure, let's solve the equation using the quadratic formula. First, we need to expand and simplify the equation:
(x + 4)(x - 1) + (x + 5)(x + 2) = 6
x^2 - x + 4x - 4 + x^2 + 2x + 5x + 10 = 6
2x^2 + 10x + 6 = 6
Now, subtract 6 from both sides to set the equation to zero:
2x^2 + 10x = 0
Now it's in the form ax^2 + bx + c = 0, where a = 2, b = 10, and c = 0. Let's plug these into the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / (2a)
x = [-10 ± √(10^2 - 4(2)(0))] / (2(2))
x = [-10 ± √(100)] / 4
x = [-10 ± 10] / 4
This gives us two possible solutions:
x = (10 - 10) / 4 = 0/4 = 0
x = (-10 - 10) / 4 = -20/4 = -5
So, the solutions are x = 0 and x = -5.
