G(4x)=x^2+4x

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


Simplifying
G(4x) = x2 + 4x

Remove parenthesis around (4x)
G * 4x = x2 + 4x

Reorder the terms for easier multiplication:
4G * x = x2 + 4x

Multiply G * x
4xG = x2 + 4x

Reorder the terms:
4xG = 4x + x2

Solving
4xG = 4x + x2

Solving for variable 'x'.

Reorder the terms:
-4x + 4xG + -1x2 = 4x + x2 + -4x + -1x2

Reorder the terms:
-4x + 4xG + -1x2 = 4x + -4x + x2 + -1x2

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + 4G + -1x) = 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 '(-4 + 4G + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + 4G + -1x = 0

Solving
-4 + 4G + -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 + 4G + 4 + -1x = 0 + 4

Reorder the terms:
-4 + 4 + 4G + -1x = 0 + 4

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

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

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

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

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

Simplifying
x = -4 + 4G
Solution
x = {0, -4 + 4G}

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