Final answer:
To find the solution to the equation -4(8 – 3x)^2 + 6x - 8, we need to simplify the expression and solve for x.
Step-by-step explanation:
To find the solution to the equation -4(8 – 3x)^2 + 6x - 8, we need to simplify the expression and solve for x.
Step 1: Distribute -4 to the terms inside the parentheses:
-4 * 8 = -32
-4 * -3x = 12x
The expression now becomes: -32 + 12x^2 + 6x - 8
Step 2: Combine like terms:
-32 - 8 = -40
12x^2 + 6x = 2x(6x + 3)
The expression now becomes: 2x(6x + 3) - 40
Step 3: Factor out common factors if possible:
2x(6x + 3) - 40 = 2x(2(3x + 1) - 20)
The expression now becomes: 2x(6x + 3) - 40 = 2x(6x + 3 - 10)
Step 4: Simplify the expression:
2x(6x - 7) - 40
The final simplified expression is: 2x(6x - 7) - 40
There is no single solution to this equation, as it is in factored form. The solution depends on the value of x.