Find the value of x and show steps.
4(3x+4)(x-4)
To find the value of x in the expression 4(3x+4)(x-4), first, expand the expression using the distributive property.
4(3x+4)(x-4)
= 4(3x)(x) - 4(3x)(4) + 4(4)(x) - 4(4)(4)
= 12x^2 - 48x + 16x - 64
= 12x^2 - 32x - 64
Now that the expression is expanded, we can simplify it further.
12x^2 - 32x - 64 = 0
Next, we need to solve the quadratic equation for x. To do this, we can either factor the equation or use the quadratic formula.
Factoring:
12x^2 - 32x - 64 = 0
4(3x^2 - 8x - 16) = 0
4(3x + 4)(x - 4) = 0
Setting each factor to zero:
3x + 4 = 0 or x - 4 = 0
3x = -4 x = 4
x = -4/3
Therefore, the two possible values for x are x = -4/3 or x = 4.