Expanding the left side of the equation, we get:
(2x + 5)^2 - (4x - 1)^2= (4x^2 + 20x + 25) - (16x^2 - 8x + 1)= 4x^2 + 20x + 25 - 16x^2 + 8x - 1= -12x^2 + 28x + 24
Setting this equal to 24:
-12x^2 + 28x + 24 = 24
Subtracting 24 from both sides:
-12x^2 + 28x = 0
Factor out a common factor of 4x:
4x(-3x + 7) = 0
Setting each factor to zero:
4x = 0 or -3x + 7 = 0
For the first factor:
4x = 0x = 0
For the second factor:
-3x + 7 = 0-3x = -7x = 7/3
Therefore, the solutions to the equation are x = 0 and x = 7/3.
Expanding the left side of the equation, we get:
(2x + 5)^2 - (4x - 1)^2
= (4x^2 + 20x + 25) - (16x^2 - 8x + 1)
= 4x^2 + 20x + 25 - 16x^2 + 8x - 1
= -12x^2 + 28x + 24
Setting this equal to 24:
-12x^2 + 28x + 24 = 24
Subtracting 24 from both sides:
-12x^2 + 28x = 0
Factor out a common factor of 4x:
4x(-3x + 7) = 0
Setting each factor to zero:
4x = 0 or -3x + 7 = 0
For the first factor:
4x = 0
x = 0
For the second factor:
-3x + 7 = 0
-3x = -7
x = 7/3
Therefore, the solutions to the equation are x = 0 and x = 7/3.