4.5(x-1)2(x-1)=0

Solution for 4.5(x-1)2(x-1)=0 equation:

Simplifying
4.5(x + -1) * 2(x + -1) = 0

Reorder the terms:
4.5(-1 + x) * 2(x + -1) = 0

Reorder the terms:
4.5(-1 + x) * 2(-1 + x) = 0

Reorder the terms for easier multiplication:
4.5 * 2(-1 + x)(-1 + x) = 0

Multiply 4.5 * 2
9(-1 + x)(-1 + x) = 0

Multiply (-1 + x) * (-1 + x)
9(-1(-1 + x) + x(-1 + x)) = 0
9((-1 * -1 + x * -1) + x(-1 + x)) = 0
9((1 + -1x) + x(-1 + x)) = 0
9(1 + -1x + (-1 * x + x * x)) = 0
9(1 + -1x + (-1x + x2)) = 0

Combine like terms: -1x + -1x = -2x
9(1 + -2x + x2) = 0
(1 * 9 + -2x * 9 + x2 * 9) = 0
(9 + -18x + 9x2) = 0

Solving
9 + -18x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(1 + -2x + x2) = 0

Factor a trinomial.
9((1 + -1x)(1 + -1x)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {1, 1}