(5a+2b)(5a+3b)=

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Solution for (5a+2b)(5a+3b)= equation: 


Simplifying
(5a + 2b)(5a + 3b) = 0

Multiply (5a + 2b) * (5a + 3b)
(5a * (5a + 3b) + 2b * (5a + 3b)) = 0
((5a * 5a + 3b * 5a) + 2b * (5a + 3b)) = 0

Reorder the terms:
((15ab + 25a2) + 2b * (5a + 3b)) = 0
((15ab + 25a2) + 2b * (5a + 3b)) = 0
(15ab + 25a2 + (5a * 2b + 3b * 2b)) = 0
(15ab + 25a2 + (10ab + 6b2)) = 0

Reorder the terms:
(15ab + 10ab + 25a2 + 6b2) = 0

Combine like terms: 15ab + 10ab = 25ab
(25ab + 25a2 + 6b2) = 0

Solving
25ab + 25a2 + 6b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + 2b)(5a + 3b) = 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 '(5a + 3b)' equal to zero and attempt to solve:

Simplifying
5a + 3b = 0

Solving
5a + 3b = 0

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

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

Combine like terms: 3b + -3b = 0
5a + 0 = 0 + -3b
5a = 0 + -3b
Remove the zero:
5a = -3b

Divide each side by '5'.
a = -0.6b

Simplifying
a = -0.6b
Solution
a = {-0.4b, -0.6b}

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