7x-3x(x-2)=3x(x+4)

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


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

Reorder the terms:
7x + -3x(-2 + x) = 3x(x + 4)
7x + (-2 * -3x + x * -3x) = 3x(x + 4)
7x + (6x + -3x2) = 3x(x + 4)

Combine like terms: 7x + 6x = 13x
13x + -3x2 = 3x(x + 4)

Reorder the terms:
13x + -3x2 = 3x(4 + x)
13x + -3x2 = (4 * 3x + x * 3x)
13x + -3x2 = (12x + 3x2)

Solving
13x + -3x2 = 12x + 3x2

Solving for variable 'x'.

Reorder the terms:
13x + -12x + -3x2 + -3x2 = 12x + 3x2 + -12x + -3x2

Combine like terms: 13x + -12x = 1x
1x + -3x2 + -3x2 = 12x + 3x2 + -12x + -3x2

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

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

Combine like terms: 12x + -12x = 0
1x + -6x2 = 0 + 3x2 + -3x2
1x + -6x2 = 3x2 + -3x2

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -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 '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 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 + -6x = 0 + -1

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

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

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
Solution
x = {0, 0.1666666667}

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