(2a+5b)(5a+2b)=

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Solution for (2a+5b)(5a+2b)= equation: 


Simplifying
(2a + 5b)(5a + 2b) = 0

Multiply (2a + 5b) * (5a + 2b)
(2a * (5a + 2b) + 5b * (5a + 2b)) = 0
((5a * 2a + 2b * 2a) + 5b * (5a + 2b)) = 0

Reorder the terms:
((4ab + 10a2) + 5b * (5a + 2b)) = 0
((4ab + 10a2) + 5b * (5a + 2b)) = 0
(4ab + 10a2 + (5a * 5b + 2b * 5b)) = 0
(4ab + 10a2 + (25ab + 10b2)) = 0

Reorder the terms:
(4ab + 25ab + 10a2 + 10b2) = 0

Combine like terms: 4ab + 25ab = 29ab
(29ab + 10a2 + 10b2) = 0

Solving
29ab + 10a2 + 10b2 = 0

Solving for variable 'a'.

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


Subproblem 1
Set the factor '(5a + 2b)' equal to zero and attempt to solve:

Simplifying
5a + 2b = 0

Solving
5a + 2b = 0

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

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

Combine like terms: 2b + -2b = 0
5a + 0 = 0 + -2b
5a = 0 + -2b
Remove the zero:
5a = -2b

Divide each side by '5'.
a = -0.4b

Simplifying
a = -0.4b

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

Simplifying
2a + 5b = 0

Solving
2a + 5b = 0

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

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

Combine like terms: 5b + -5b = 0
2a + 0 = 0 + -5b
2a = 0 + -5b
Remove the zero:
2a = -5b

Divide each side by '2'.
a = -2.5b

Simplifying
a = -2.5b
Solution
a = {-0.4b, -2.5b}

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