3x(x-7)=6(x^2)-22x

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Solution for 3x(x-7)=6(x^2)-22x equation: 


Simplifying
3x(x + -7) = 6(x2) + -22x

Reorder the terms:
3x(-7 + x) = 6(x2) + -22x
(-7 * 3x + x * 3x) = 6(x2) + -22x
(-21x + 3x2) = 6(x2) + -22x

Reorder the terms:
-21x + 3x2 = -22x + 6x2

Solving
-21x + 3x2 = -22x + 6x2

Solving for variable 'x'.

Reorder the terms:
-21x + 22x + 3x2 + -6x2 = -22x + 6x2 + 22x + -6x2

Combine like terms: -21x + 22x = 1x
1x + 3x2 + -6x2 = -22x + 6x2 + 22x + -6x2

Combine like terms: 3x2 + -6x2 = -3x2
1x + -3x2 = -22x + 6x2 + 22x + -6x2

Reorder the terms:
1x + -3x2 = -22x + 22x + 6x2 + -6x2

Combine like terms: -22x + 22x = 0
1x + -3x2 = 0 + 6x2 + -6x2
1x + -3x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
1x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -3x) = 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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, 0.3333333333}

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