(2x+4)(2x+1)=4

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Solution for (2x+4)(2x+1)=4 equation: 


Simplifying
(2x + 4)(2x + 1) = 4

Reorder the terms:
(4 + 2x)(2x + 1) = 4

Reorder the terms:
(4 + 2x)(1 + 2x) = 4

Multiply (4 + 2x) * (1 + 2x)
(4(1 + 2x) + 2x * (1 + 2x)) = 4
((1 * 4 + 2x * 4) + 2x * (1 + 2x)) = 4
((4 + 8x) + 2x * (1 + 2x)) = 4
(4 + 8x + (1 * 2x + 2x * 2x)) = 4
(4 + 8x + (2x + 4x2)) = 4

Combine like terms: 8x + 2x = 10x
(4 + 10x + 4x2) = 4

Add '-4' to each side of the equation.
4 + 10x + -4 + 4x2 = 4 + -4

Reorder the terms:
4 + -4 + 10x + 4x2 = 4 + -4

Combine like terms: 4 + -4 = 0
0 + 10x + 4x2 = 4 + -4
10x + 4x2 = 4 + -4

Combine like terms: 4 + -4 = 0
10x + 4x2 = 0

Solving
10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(5 + 2x) = 0

Ignore the factor 2.

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 '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {0, -2.5}

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