6x(2-x)+4=1-(x-3)

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Solution for 6x(2-x)+4=1-(x-3) equation: 


Simplifying
6x(2 + -1x) + 4 = 1 + -1(x + -3)
(2 * 6x + -1x * 6x) + 4 = 1 + -1(x + -3)
(12x + -6x2) + 4 = 1 + -1(x + -3)

Reorder the terms:
4 + 12x + -6x2 = 1 + -1(x + -3)

Reorder the terms:
4 + 12x + -6x2 = 1 + -1(-3 + x)
4 + 12x + -6x2 = 1 + (-3 * -1 + x * -1)
4 + 12x + -6x2 = 1 + (3 + -1x)

Combine like terms: 1 + 3 = 4
4 + 12x + -6x2 = 4 + -1x

Add '-4' to each side of the equation.
4 + 12x + -4 + -6x2 = 4 + -4 + -1x

Reorder the terms:
4 + -4 + 12x + -6x2 = 4 + -4 + -1x

Combine like terms: 4 + -4 = 0
0 + 12x + -6x2 = 4 + -4 + -1x
12x + -6x2 = 4 + -4 + -1x

Combine like terms: 4 + -4 = 0
12x + -6x2 = 0 + -1x
12x + -6x2 = -1x

Solving
12x + -6x2 = -1x

Solving for variable 'x'.

Reorder the terms:
12x + x + -6x2 = -1x + x

Combine like terms: 12x + x = 13x
13x + -6x2 = -1x + x

Combine like terms: -1x + x = 0
13x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + -6x) = 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 '(13 + -6x)' equal to zero and attempt to solve:

Simplifying
13 + -6x = 0

Solving
13 + -6x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -6x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -6x = 0 + -13
-6x = 0 + -13

Combine like terms: 0 + -13 = -13
-6x = -13

Divide each side by '-6'.
x = 2.166666667

Simplifying
x = 2.166666667
Solution
x = {0, 2.166666667}

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