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

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


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

Reorder the terms for easier multiplication:
x(6 + -1x) = (x + 3)(x)
(6 * x + -1x * x) = (x + 3)(x)
(6x + -1x2) = (x + 3)(x)

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

Reorder the terms for easier multiplication:
6x + -1x2 = x(3 + x)
6x + -1x2 = (3 * x + x * x)
6x + -1x2 = (3x + x2)

Solving
6x + -1x2 = 3x + x2

Solving for variable 'x'.

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

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

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

Reorder the terms:
3x + -2x2 = 3x + -3x + x2 + -1x2

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + -2x) = 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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, 1.5}

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