3(x^2-4x+4)=48

Solution for 3(x^2-4x+4)=48 equation:

Simplifying
3(x2 + -4x + 4) = 48

Reorder the terms:
3(4 + -4x + x2) = 48
(4 * 3 + -4x * 3 + x2 * 3) = 48
(12 + -12x + 3x2) = 48

Solving
12 + -12x + 3x2 = 48

Solving for variable 'x'.

Reorder the terms:
12 + -48 + -12x + 3x2 = 48 + -48

Combine like terms: 12 + -48 = -36
-36 + -12x + 3x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-36 + -12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -4x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(6 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2, 6}