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

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


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

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

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

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

Combine like terms: 4x + 2x = 6x
(2 + 6x + 4x2) = 0

Solving
2 + 6x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 3x + 2x2) = 0

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

Ignore the factor 2.

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1

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 = {-1, -0.5}

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