3(2x+1)+5x(2x+1)=0

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Solution for 3(2x+1)+5x(2x+1)=0 equation: 


Simplifying
3(2x + 1) + 5x(2x + 1) = 0

Reorder the terms:
3(1 + 2x) + 5x(2x + 1) = 0
(1 * 3 + 2x * 3) + 5x(2x + 1) = 0
(3 + 6x) + 5x(2x + 1) = 0

Reorder the terms:
3 + 6x + 5x(1 + 2x) = 0
3 + 6x + (1 * 5x + 2x * 5x) = 0
3 + 6x + (5x + 10x2) = 0

Combine like terms: 6x + 5x = 11x
3 + 11x + 10x2 = 0

Solving
3 + 11x + 10x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + 5x)(1 + 2x) = 0


Subproblem 1
Set the factor '(3 + 5x)' equal to zero and attempt to solve:

Simplifying
3 + 5x = 0

Solving
3 + 5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5x = 0 + -3
5x = 0 + -3

Combine like terms: 0 + -3 = -3
5x = -3

Divide each side by '5'.
x = -0.6

Simplifying
x = -0.6

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 = {-0.6, -0.5}

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