3-2x(x-1)=5-(-2x+4x)

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Solution for 3-2x(x-1)=5-(-2x+4x) equation: 


Simplifying
3 + -2x(x + -1) = 5 + -1(-2x + 4x)

Reorder the terms:
3 + -2x(-1 + x) = 5 + -1(-2x + 4x)
3 + (-1 * -2x + x * -2x) = 5 + -1(-2x + 4x)
3 + (2x + -2x2) = 5 + -1(-2x + 4x)

Combine like terms: -2x + 4x = 2x
3 + 2x + -2x2 = 5 + -1(2x)

Remove parenthesis around (2x)
3 + 2x + -2x2 = 5 + -1 * 2x

Multiply -1 * 2
3 + 2x + -2x2 = 5 + -2x

Solving
3 + 2x + -2x2 = 5 + -2x

Solving for variable 'x'.

Reorder the terms:
3 + -5 + 2x + 2x + -2x2 = 5 + -2x + -5 + 2x

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

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

Reorder the terms:
-2 + 4x + -2x2 = 5 + -5 + -2x + 2x

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

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

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

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

Ignore the factor 2.

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

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

Combine like terms: 0 + 1 = 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}

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