6x-x(3x+x-7)=3x(x+4)

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


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

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

Combine like terms: 3x + x = 4x
6x + -1x(-7 + 4x) = 3x(x + 4)
6x + (-7 * -1x + 4x * -1x) = 3x(x + 4)
6x + (7x + -4x2) = 3x(x + 4)

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

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

Solving
13x + -4x2 = 12x + 3x2

Solving for variable 'x'.

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

Combine like terms: 13x + -12x = 1x
1x + -4x2 + -3x2 = 12x + 3x2 + -12x + -3x2

Combine like terms: -4x2 + -3x2 = -7x2
1x + -7x2 = 12x + 3x2 + -12x + -3x2

Reorder the terms:
1x + -7x2 = 12x + -12x + 3x2 + -3x2

Combine like terms: 12x + -12x = 0
1x + -7x2 = 0 + 3x2 + -3x2
1x + -7x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
1x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -7x) = 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 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 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 + -7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x = 0 + -1
-7x = 0 + -1

Combine like terms: 0 + -1 = -1
-7x = -1

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429
Solution
x = {0, 0.1428571429}

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