To solve this equation, we will first expand both sides using the distributive property.
Expanding the left side:(-8x)(4x) + (-8x)(3) + (-1)(4x) + (-1)(3)-32x^2 - 24x - 4x - 3
Expanding the right side:(12x)(x) + (12x)(-1) + (-5)(x) + (-5)(-1)12x^2 - 12x - 5x + 5
Now we can simplify both sides of the equation:
-32x^2 - 24x - 4x - 3 = 12x^2 - 12x - 5x + 5
Combining like terms:
-32x^2 - 28x - 3 = 12x^2 - 17x + 5
Next, we will move all terms to one side of the equation:
-32x^2 - 28x - 3 - 12x^2 + 17x - 5 = 0
Combine like terms:
-44x^2 - 11x - 8 = 0
Now we have a quadratic equation that we can solve using the quadratic formula:
x = (-(-11) ± sqrt((-11)^2 - 4(-44)(-8))) / 2(-44)
x = (11 ± sqrt(121 - 1408)) / -88
x = (11 ± sqrt(-1287)) / -88
Since the square root of a negative number results in imaginary solutions, this quadratic equation does not have real solutions.
To solve this equation, we will first expand both sides using the distributive property.
Expanding the left side:
(-8x)(4x) + (-8x)(3) + (-1)(4x) + (-1)(3)
-32x^2 - 24x - 4x - 3
Expanding the right side:
(12x)(x) + (12x)(-1) + (-5)(x) + (-5)(-1)
12x^2 - 12x - 5x + 5
Now we can simplify both sides of the equation:
-32x^2 - 24x - 4x - 3 = 12x^2 - 12x - 5x + 5
Combining like terms:
-32x^2 - 28x - 3 = 12x^2 - 17x + 5
Next, we will move all terms to one side of the equation:
-32x^2 - 28x - 3 - 12x^2 + 17x - 5 = 0
Combine like terms:
-44x^2 - 11x - 8 = 0
Now we have a quadratic equation that we can solve using the quadratic formula:
x = (-(-11) ± sqrt((-11)^2 - 4(-44)(-8))) / 2(-44)
x = (11 ± sqrt(121 - 1408)) / -88
x = (11 ± sqrt(-1287)) / -88
Since the square root of a negative number results in imaginary solutions, this quadratic equation does not have real solutions.