2(2x+5)(2x+1)=0

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Solution for 2(2x+5)(2x+1)=0 equation: 


Simplifying
2(2x + 5)(2x + 1) = 0

Reorder the terms:
2(5 + 2x)(2x + 1) = 0

Reorder the terms:
2(5 + 2x)(1 + 2x) = 0

Multiply (5 + 2x) * (1 + 2x)
2(5(1 + 2x) + 2x * (1 + 2x)) = 0
2((1 * 5 + 2x * 5) + 2x * (1 + 2x)) = 0
2((5 + 10x) + 2x * (1 + 2x)) = 0
2(5 + 10x + (1 * 2x + 2x * 2x)) = 0
2(5 + 10x + (2x + 4x2)) = 0

Combine like terms: 10x + 2x = 12x
2(5 + 12x + 4x2) = 0
(5 * 2 + 12x * 2 + 4x2 * 2) = 0
(10 + 24x + 8x2) = 0

Solving
10 + 24x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 12x + 4x2) = 0

Factor a trinomial.
2((5 + 2x)(1 + 2x)) = 0

Ignore the factor 2.

Subproblem 1
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

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 = {-2.5, -0.5}

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