(7a-5)(5a-4)=0

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Solution for (7a-5)(5a-4)=0 equation: 


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

Reorder the terms:
(-5 + 7a)(5a + -4) = 0

Reorder the terms:
(-5 + 7a)(-4 + 5a) = 0

Multiply (-5 + 7a) * (-4 + 5a)
(-5(-4 + 5a) + 7a * (-4 + 5a)) = 0
((-4 * -5 + 5a * -5) + 7a * (-4 + 5a)) = 0
((20 + -25a) + 7a * (-4 + 5a)) = 0
(20 + -25a + (-4 * 7a + 5a * 7a)) = 0
(20 + -25a + (-28a + 35a2)) = 0

Combine like terms: -25a + -28a = -53a
(20 + -53a + 35a2) = 0

Solving
20 + -53a + 35a2 = 0

Solving for variable 'a'.

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


Subproblem 1
Set the factor '(5 + -7a)' equal to zero and attempt to solve:

Simplifying
5 + -7a = 0

Solving
5 + -7a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -7a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7a = 0 + -5
-7a = 0 + -5

Combine like terms: 0 + -5 = -5
-7a = -5

Divide each side by '-7'.
a = 0.7142857143

Simplifying
a = 0.7142857143

Subproblem 2
Set the factor '(4 + -5a)' equal to zero and attempt to solve:

Simplifying
4 + -5a = 0

Solving
4 + -5a = 0

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

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

Combine like terms: 4 + -4 = 0
0 + -5a = 0 + -4
-5a = 0 + -4

Combine like terms: 0 + -4 = -4
-5a = -4

Divide each side by '-5'.
a = 0.8

Simplifying
a = 0.8
Solution
a = {0.7142857143, 0.8}

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