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

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


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

Reorder the terms:
5x(1 + 2x) + 2x + 1 = 0
(1 * 5x + 2x * 5x) + 2x + 1 = 0
(5x + 10x2) + 2x + 1 = 0

Reorder the terms:
1 + 5x + 2x + 10x2 = 0

Combine like terms: 5x + 2x = 7x
1 + 7x + 10x2 = 0

Solving
1 + 7x + 10x2 = 0

Solving for variable 'x'.

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


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

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-0.5, -0.2}

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