3(x-4)-2(3x-6)=2x-7x(7x-1)

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Solution for 3(x-4)-2(3x-6)=2x-7x(7x-1) equation: 


Simplifying
3(x + -4) + -2(3x + -6) = 2x + -7x(7x + -1)

Reorder the terms:
3(-4 + x) + -2(3x + -6) = 2x + -7x(7x + -1)
(-4 * 3 + x * 3) + -2(3x + -6) = 2x + -7x(7x + -1)
(-12 + 3x) + -2(3x + -6) = 2x + -7x(7x + -1)

Reorder the terms:
-12 + 3x + -2(-6 + 3x) = 2x + -7x(7x + -1)
-12 + 3x + (-6 * -2 + 3x * -2) = 2x + -7x(7x + -1)
-12 + 3x + (12 + -6x) = 2x + -7x(7x + -1)

Reorder the terms:
-12 + 12 + 3x + -6x = 2x + -7x(7x + -1)

Combine like terms: -12 + 12 = 0
0 + 3x + -6x = 2x + -7x(7x + -1)
3x + -6x = 2x + -7x(7x + -1)

Combine like terms: 3x + -6x = -3x
-3x = 2x + -7x(7x + -1)

Reorder the terms:
-3x = 2x + -7x(-1 + 7x)
-3x = 2x + (-1 * -7x + 7x * -7x)
-3x = 2x + (7x + -49x2)

Combine like terms: 2x + 7x = 9x
-3x = 9x + -49x2

Solving
-3x = 9x + -49x2

Solving for variable 'x'.

Combine like terms: -3x + -9x = -12x
-12x + 49x2 = 9x + -49x2 + -9x + 49x2

Reorder the terms:
-12x + 49x2 = 9x + -9x + -49x2 + 49x2

Combine like terms: 9x + -9x = 0
-12x + 49x2 = 0 + -49x2 + 49x2
-12x + 49x2 = -49x2 + 49x2

Combine like terms: -49x2 + 49x2 = 0
-12x + 49x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-12 + 49x) = 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 '(-12 + 49x)' equal to zero and attempt to solve:

Simplifying
-12 + 49x = 0

Solving
-12 + 49x = 0

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

Add '12' to each side of the equation.
-12 + 12 + 49x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 49x = 0 + 12
49x = 0 + 12

Combine like terms: 0 + 12 = 12
49x = 12

Divide each side by '49'.
x = 0.2448979592

Simplifying
x = 0.2448979592
Solution
x = {0, 0.2448979592}

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