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

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


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

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

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

Solving
2x + x2 = 4 + 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + 2x + -6x + x2 + -2x2 = 4 + 6x + 2x2 + -4 + -6x + -2x2

Combine like terms: 2x + -6x = -4x
-4 + -4x + x2 + -2x2 = 4 + 6x + 2x2 + -4 + -6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-4 + -4x + -1x2 = 4 + 6x + 2x2 + -4 + -6x + -2x2

Reorder the terms:
-4 + -4x + -1x2 = 4 + -4 + 6x + -6x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-4 + -4x + -1x2 = 0 + 6x + -6x + 2x2 + -2x2
-4 + -4x + -1x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
-4 + -4x + -1x2 = 0 + 2x2 + -2x2
-4 + -4x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + -4x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 4x + x2) = 0

Factor a trinomial.
-1((2 + x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {-2, -2}

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