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

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


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

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

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

Multiply (2 + 5x) * (2 + 3x)
(2(2 + 3x) + 5x * (2 + 3x)) = 0
((2 * 2 + 3x * 2) + 5x * (2 + 3x)) = 0
((4 + 6x) + 5x * (2 + 3x)) = 0
(4 + 6x + (2 * 5x + 3x * 5x)) = 0
(4 + 6x + (10x + 15x2)) = 0

Combine like terms: 6x + 10x = 16x
(4 + 16x + 15x2) = 0

Solving
4 + 16x + 15x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
Set the factor '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {-0.6666666667, -0.4}

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