x(x+6)-x(7-2x)=0

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Solution for x(x+6)-x(7-2x)=0 equation: 


Simplifying
x(x + 6) + -1x(7 + -2x) = 0

Reorder the terms:
x(6 + x) + -1x(7 + -2x) = 0
(6 * x + x * x) + -1x(7 + -2x) = 0
(6x + x2) + -1x(7 + -2x) = 0
6x + x2 + (7 * -1x + -2x * -1x) = 0
6x + x2 + (-7x + 2x2) = 0

Reorder the terms:
6x + -7x + x2 + 2x2 = 0

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

Combine like terms: x2 + 2x2 = 3x2
-1x + 3x2 = 0

Solving
-1x + 3x2 = 0

Solving for variable 'x'.

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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