(4a-5b)(7a-6b)=

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Solution for (4a-5b)(7a-6b)= equation: 


Simplifying
(4a + -5b)(7a + -6b) = 0

Multiply (4a + -5b) * (7a + -6b)
(4a * (7a + -6b) + -5b * (7a + -6b)) = 0
((7a * 4a + -6b * 4a) + -5b * (7a + -6b)) = 0

Reorder the terms:
((-24ab + 28a2) + -5b * (7a + -6b)) = 0
((-24ab + 28a2) + -5b * (7a + -6b)) = 0
(-24ab + 28a2 + (7a * -5b + -6b * -5b)) = 0
(-24ab + 28a2 + (-35ab + 30b2)) = 0

Reorder the terms:
(-24ab + -35ab + 28a2 + 30b2) = 0

Combine like terms: -24ab + -35ab = -59ab
(-59ab + 28a2 + 30b2) = 0

Solving
-59ab + 28a2 + 30b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -5b)(7a + -6b) = 0


Subproblem 1
Set the factor '(4a + -5b)' equal to zero and attempt to solve:

Simplifying
4a + -5b = 0

Solving
4a + -5b = 0

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

Add '5b' to each side of the equation.
4a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
4a + 0 = 0 + 5b
4a = 0 + 5b
Remove the zero:
4a = 5b

Divide each side by '4'.
a = 1.25b

Simplifying
a = 1.25b

Subproblem 2
Set the factor '(7a + -6b)' equal to zero and attempt to solve:

Simplifying
7a + -6b = 0

Solving
7a + -6b = 0

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

Add '6b' to each side of the equation.
7a + -6b + 6b = 0 + 6b

Combine like terms: -6b + 6b = 0
7a + 0 = 0 + 6b
7a = 0 + 6b
Remove the zero:
7a = 6b

Divide each side by '7'.
a = 0.8571428571b

Simplifying
a = 0.8571428571b
Solution
a = {1.25b, 0.8571428571b}

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