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

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


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

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

Reorder the terms:
2x + x2 = 4(2 + x)
2x + x2 = (2 * 4 + x * 4)
2x + x2 = (8 + 4x)

Solving
2x + x2 = 8 + 4x

Solving for variable 'x'.

Reorder the terms:
-8 + 2x + -4x + x2 = 8 + 4x + -8 + -4x

Combine like terms: 2x + -4x = -2x
-8 + -2x + x2 = 8 + 4x + -8 + -4x

Reorder the terms:
-8 + -2x + x2 = 8 + -8 + 4x + -4x

Combine like terms: 8 + -8 = 0
-8 + -2x + x2 = 0 + 4x + -4x
-8 + -2x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-8 + -2x + x2 = 0

Factor a trinomial.
(-2 + -1x)(4 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2, 4}

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