x(x+2)=38(x+4)+8

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Solution for x(x+2)=38(x+4)+8 equation: 


Simplifying
x(x + 2) = 38(x + 4) + 8

Reorder the terms:
x(2 + x) = 38(x + 4) + 8
(2 * x + x * x) = 38(x + 4) + 8
(2x + x2) = 38(x + 4) + 8

Reorder the terms:
2x + x2 = 38(4 + x) + 8
2x + x2 = (4 * 38 + x * 38) + 8
2x + x2 = (152 + 38x) + 8

Reorder the terms:
2x + x2 = 152 + 8 + 38x

Combine like terms: 152 + 8 = 160
2x + x2 = 160 + 38x

Solving
2x + x2 = 160 + 38x

Solving for variable 'x'.

Reorder the terms:
-160 + 2x + -38x + x2 = 160 + 38x + -160 + -38x

Combine like terms: 2x + -38x = -36x
-160 + -36x + x2 = 160 + 38x + -160 + -38x

Reorder the terms:
-160 + -36x + x2 = 160 + -160 + 38x + -38x

Combine like terms: 160 + -160 = 0
-160 + -36x + x2 = 0 + 38x + -38x
-160 + -36x + x2 = 38x + -38x

Combine like terms: 38x + -38x = 0
-160 + -36x + x2 = 0

Factor a trinomial.
(-4 + -1x)(40 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(40 + -1x)' equal to zero and attempt to solve:

Simplifying
40 + -1x = 0

Solving
40 + -1x = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1x = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1x = 0 + -40
-1x = 0 + -40

Combine like terms: 0 + -40 = -40
-1x = -40

Divide each side by '-1'.
x = 40

Simplifying
x = 40
Solution
x = {-4, 40}

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