(3a-7)(a-7)=0

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Solution for (3a-7)(a-7)=0 equation: 


Simplifying
(3a + -7)(a + -7) = 0

Reorder the terms:
(-7 + 3a)(a + -7) = 0

Reorder the terms:
(-7 + 3a)(-7 + a) = 0

Multiply (-7 + 3a) * (-7 + a)
(-7(-7 + a) + 3a * (-7 + a)) = 0
((-7 * -7 + a * -7) + 3a * (-7 + a)) = 0
((49 + -7a) + 3a * (-7 + a)) = 0
(49 + -7a + (-7 * 3a + a * 3a)) = 0
(49 + -7a + (-21a + 3a2)) = 0

Combine like terms: -7a + -21a = -28a
(49 + -28a + 3a2) = 0

Solving
49 + -28a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7 + -3a)(7 + -1a) = 0


Subproblem 1
Set the factor '(7 + -3a)' equal to zero and attempt to solve:

Simplifying
7 + -3a = 0

Solving
7 + -3a = 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 + -3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3a = 0 + -7
-3a = 0 + -7

Combine like terms: 0 + -7 = -7
-3a = -7

Divide each side by '-3'.
a = 2.333333333

Simplifying
a = 2.333333333

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 = {2.333333333, 7}

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