(3x-1)2+2x(1-x)+2=x-7(1-x)x

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Solution for (3x-1)2+2x(1-x)+2=x-7(1-x)x equation:


Simplifying
(3x + -1) * 2 + 2x(1 + -1x) + 2 = x + -7(1 + -1x) * x

Reorder the terms:
(-1 + 3x) * 2 + 2x(1 + -1x) + 2 = x + -7(1 + -1x) * x

Reorder the terms for easier multiplication:
2(-1 + 3x) + 2x(1 + -1x) + 2 = x + -7(1 + -1x) * x
(-1 * 2 + 3x * 2) + 2x(1 + -1x) + 2 = x + -7(1 + -1x) * x
(-2 + 6x) + 2x(1 + -1x) + 2 = x + -7(1 + -1x) * x
-2 + 6x + (1 * 2x + -1x * 2x) + 2 = x + -7(1 + -1x) * x
-2 + 6x + (2x + -2x2) + 2 = x + -7(1 + -1x) * x

Reorder the terms:
-2 + 2 + 6x + 2x + -2x2 = x + -7(1 + -1x) * x

Combine like terms: -2 + 2 = 0
0 + 6x + 2x + -2x2 = x + -7(1 + -1x) * x
6x + 2x + -2x2 = x + -7(1 + -1x) * x

Combine like terms: 6x + 2x = 8x
8x + -2x2 = x + -7(1 + -1x) * x

Reorder the terms for easier multiplication:
8x + -2x2 = x + -7x(1 + -1x)
8x + -2x2 = x + (1 * -7x + -1x * -7x)
8x + -2x2 = x + (-7x + 7x2)

Combine like terms: x + -7x = -6x
8x + -2x2 = -6x + 7x2

Solving
8x + -2x2 = -6x + 7x2

Solving for variable 'x'.

Reorder the terms:
8x + 6x + -2x2 + -7x2 = -6x + 7x2 + 6x + -7x2

Combine like terms: 8x + 6x = 14x
14x + -2x2 + -7x2 = -6x + 7x2 + 6x + -7x2

Combine like terms: -2x2 + -7x2 = -9x2
14x + -9x2 = -6x + 7x2 + 6x + -7x2

Reorder the terms:
14x + -9x2 = -6x + 6x + 7x2 + -7x2

Combine like terms: -6x + 6x = 0
14x + -9x2 = 0 + 7x2 + -7x2
14x + -9x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
14x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(14 + -9x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(14 + -9x)' equal to zero and attempt to solve:

Simplifying
14 + -9x = 0

Solving
14 + -9x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -9x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -9x = 0 + -14
-9x = 0 + -14

Combine like terms: 0 + -14 = -14
-9x = -14

Divide each side by '-9'.
x = 1.555555556

Simplifying
x = 1.555555556
Solution
x = {0, 1.555555556}

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