4(2x+1)(2x+1)=0

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Solution for 4(2x+1)(2x+1)=0 equation: 


Simplifying
4(2x + 1)(2x + 1) = 0

Reorder the terms:
4(1 + 2x)(2x + 1) = 0

Reorder the terms:
4(1 + 2x)(1 + 2x) = 0

Multiply (1 + 2x) * (1 + 2x)
4(1(1 + 2x) + 2x * (1 + 2x)) = 0
4((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 0
4((1 + 2x) + 2x * (1 + 2x)) = 0
4(1 + 2x + (1 * 2x + 2x * 2x)) = 0
4(1 + 2x + (2x + 4x2)) = 0

Combine like terms: 2x + 2x = 4x
4(1 + 4x + 4x2) = 0
(1 * 4 + 4x * 4 + 4x2 * 4) = 0
(4 + 16x + 16x2) = 0

Solving
4 + 16x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 4x + 4x2) = 0

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

Ignore the factor 4.

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

Simplifying
1 + 2x = 0

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

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

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

Simplifying
1 + 2x = 0

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

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-0.5, -0.5}

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