x(2x+3)=6x-x^2

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Solution for x(2x+3)=6x-x^2 equation: 


Simplifying
x(2x + 3) = 6x + -1x2

Reorder the terms:
x(3 + 2x) = 6x + -1x2
(3 * x + 2x * x) = 6x + -1x2
(3x + 2x2) = 6x + -1x2

Solving
3x + 2x2 = 6x + -1x2

Solving for variable 'x'.

Reorder the terms:
3x + -6x + 2x2 + x2 = 6x + -1x2 + -6x + x2

Combine like terms: 3x + -6x = -3x
-3x + 2x2 + x2 = 6x + -1x2 + -6x + x2

Combine like terms: 2x2 + x2 = 3x2
-3x + 3x2 = 6x + -1x2 + -6x + x2

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

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

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

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-1 + x) = 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 '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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