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

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


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

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

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

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

Combine like terms: -25ab + 6ab = -19ab
(-19ab + 15a2 + -10b2) = 0

Solving
-19ab + 15a2 + -10b2 = 0

Solving for variable 'a'.

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


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

Simplifying
3a + -5b = 0

Solving
3a + -5b = 0

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

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

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

Divide each side by '3'.
a = 1.666666667b

Simplifying
a = 1.666666667b

Subproblem 2
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
Solution
a = {1.666666667b, -0.4b}

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