(2a-5)(a-7)=0

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Solution for (2a-5)(a-7)=0 equation: 


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

Reorder the terms:
(-5 + 2a)(a + -7) = 0

Reorder the terms:
(-5 + 2a)(-7 + a) = 0

Multiply (-5 + 2a) * (-7 + a)
(-5(-7 + a) + 2a * (-7 + a)) = 0
((-7 * -5 + a * -5) + 2a * (-7 + a)) = 0
((35 + -5a) + 2a * (-7 + a)) = 0
(35 + -5a + (-7 * 2a + a * 2a)) = 0
(35 + -5a + (-14a + 2a2)) = 0

Combine like terms: -5a + -14a = -19a
(35 + -19a + 2a2) = 0

Solving
35 + -19a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5 + -2a)(7 + -1a) = 0


Subproblem 1
Set the factor '(5 + -2a)' equal to zero and attempt to solve:

Simplifying
5 + -2a = 0

Solving
5 + -2a = 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 + -2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2a = 0 + -5
-2a = 0 + -5

Combine like terms: 0 + -5 = -5
-2a = -5

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5

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

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {2.5, 7}

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