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

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


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

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

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

Multiply (5 + 2x) * (2 + 5x)
(5(2 + 5x) + 2x * (2 + 5x)) = 0
((2 * 5 + 5x * 5) + 2x * (2 + 5x)) = 0
((10 + 25x) + 2x * (2 + 5x)) = 0
(10 + 25x + (2 * 2x + 5x * 2x)) = 0
(10 + 25x + (4x + 10x2)) = 0

Combine like terms: 25x + 4x = 29x
(10 + 29x + 10x2) = 0

Solving
10 + 29x + 10x2 = 0

Solving for variable 'x'.

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


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 '(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 = {-2.5, -0.4}

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