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

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


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

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

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

Remove parenthesis around (13x)
-6x + 7x2 = 13x(x + -3)

Reorder the terms:
-6x + 7x2 = 13x(-3 + x)
-6x + 7x2 = (-3 * 13x + x * 13x)
-6x + 7x2 = (-39x + 13x2)

Solving
-6x + 7x2 = -39x + 13x2

Solving for variable 'x'.

Reorder the terms:
-6x + 39x + 7x2 + -13x2 = -39x + 13x2 + 39x + -13x2

Combine like terms: -6x + 39x = 33x
33x + 7x2 + -13x2 = -39x + 13x2 + 39x + -13x2

Combine like terms: 7x2 + -13x2 = -6x2
33x + -6x2 = -39x + 13x2 + 39x + -13x2

Reorder the terms:
33x + -6x2 = -39x + 39x + 13x2 + -13x2

Combine like terms: -39x + 39x = 0
33x + -6x2 = 0 + 13x2 + -13x2
33x + -6x2 = 13x2 + -13x2

Combine like terms: 13x2 + -13x2 = 0
33x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(11 + -2x) = 0

Ignore the factor 3.

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 '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {0, 5.5}

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