(5a+3b)(7a-2b)=

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Solution for (5a+3b)(7a-2b)= equation: 


Simplifying
(5a + 3b)(7a + -2b) = 0

Multiply (5a + 3b) * (7a + -2b)
(5a * (7a + -2b) + 3b * (7a + -2b)) = 0
((7a * 5a + -2b * 5a) + 3b * (7a + -2b)) = 0

Reorder the terms:
((-10ab + 35a2) + 3b * (7a + -2b)) = 0
((-10ab + 35a2) + 3b * (7a + -2b)) = 0
(-10ab + 35a2 + (7a * 3b + -2b * 3b)) = 0
(-10ab + 35a2 + (21ab + -6b2)) = 0

Reorder the terms:
(-10ab + 21ab + 35a2 + -6b2) = 0

Combine like terms: -10ab + 21ab = 11ab
(11ab + 35a2 + -6b2) = 0

Solving
11ab + 35a2 + -6b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7a + -2b)(5a + 3b) = 0


Subproblem 1
Set the factor '(7a + -2b)' equal to zero and attempt to solve:

Simplifying
7a + -2b = 0

Solving
7a + -2b = 0

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

Add '2b' to each side of the equation.
7a + -2b + 2b = 0 + 2b

Combine like terms: -2b + 2b = 0
7a + 0 = 0 + 2b
7a = 0 + 2b
Remove the zero:
7a = 2b

Divide each side by '7'.
a = 0.2857142857b

Simplifying
a = 0.2857142857b

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 = {0.2857142857b, -0.6b}

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