0=(x-3)(3x-3)
To solve the equation (0=(x-3)(3x-3)), we can set each factor equal to zero and solve for x.
Setting x-3=0, we have:
x-3=0
x=3
Setting 3x-3=0, we have:
3x-3=0
3x=3
x=1
Therefore, the solutions to the equation are x=3 and x=1.
To solve the equation 0=(x-3)(3x-3):
Step 1: Expand the equation.
0 = (x * 3x) - (x * 3) - (3 * 3x) + (3 * 3)
Simplifying further:
0 = 3x^2 - 3x - 9x + 9
Step 2: Combine like terms.
0 = 3x^2 - 12x + 9
Step 3: Set the equation equal to zero by moving all terms to one side.
3x^2 - 12x + 9 = 0
Step 4: If possible, factor the equation.
Since the equation cannot be easily factored, we will solve it using the quadratic formula.
Step 5: Apply the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 3, b = -12, and c = 9.
Using the values in the quadratic formula, we have:
x = (-(-12) ± √((-12)^2 - 4 * 3 * 9)) / (2 * 3)
x = (12 ± √(144 - 108)) / 6
x = (12 ± √36) / 6
x = (12 ± 6) / 6
Step 6: Simplify the solutions.
We have two possible solutions:
x1 = (12 + 6) / 6 = 18 / 6 = 3
x2 = (12 - 6) / 6 = 6 / 6 = 1
Therefore, the solutions to the equation 0=(x-3)(3x-3) are x = 3 and x = 1.