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

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


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

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

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

Solving
8x + 4x2 = 8 + 4x

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + x + x2) = 0

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

Ignore the factor 4.

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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-2, 1}

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