3(1-x)+2(x-1)(x-1)=0

Solution for 3(1-x)+2(x-1)(x-1)=0 equation:

Simplifying
3(1 + -1x) + 2(x + -1)(x + -1) = 0
(1 * 3 + -1x * 3) + 2(x + -1)(x + -1) = 0
(3 + -3x) + 2(x + -1)(x + -1) = 0

Reorder the terms:
3 + -3x + 2(-1 + x)(x + -1) = 0

Reorder the terms:
3 + -3x + 2(-1 + x)(-1 + x) = 0

Multiply (-1 + x) * (-1 + x)
3 + -3x + 2(-1(-1 + x) + x(-1 + x)) = 0
3 + -3x + 2((-1 * -1 + x * -1) + x(-1 + x)) = 0
3 + -3x + 2((1 + -1x) + x(-1 + x)) = 0
3 + -3x + 2(1 + -1x + (-1 * x + x * x)) = 0
3 + -3x + 2(1 + -1x + (-1x + x2)) = 0

Combine like terms: -1x + -1x = -2x
3 + -3x + 2(1 + -2x + x2) = 0
3 + -3x + (1 * 2 + -2x * 2 + x2 * 2) = 0
3 + -3x + (2 + -4x + 2x2) = 0

Reorder the terms:
3 + 2 + -3x + -4x + 2x2 = 0

Combine like terms: 3 + 2 = 5
5 + -3x + -4x + 2x2 = 0

Combine like terms: -3x + -4x = -7x
5 + -7x + 2x2 = 0

Solving
5 + -7x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(5 + -2x) = 0

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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1, 2.5}