(a-8)(6a-7)=0

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Solution for (a-8)(6a-7)=0 equation: 


Simplifying
(a + -8)(6a + -7) = 0

Reorder the terms:
(-8 + a)(6a + -7) = 0

Reorder the terms:
(-8 + a)(-7 + 6a) = 0

Multiply (-8 + a) * (-7 + 6a)
(-8(-7 + 6a) + a(-7 + 6a)) = 0
((-7 * -8 + 6a * -8) + a(-7 + 6a)) = 0
((56 + -48a) + a(-7 + 6a)) = 0
(56 + -48a + (-7 * a + 6a * a)) = 0
(56 + -48a + (-7a + 6a2)) = 0

Combine like terms: -48a + -7a = -55a
(56 + -55a + 6a2) = 0

Solving
56 + -55a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7 + -6a)(8 + -1a) = 0


Subproblem 1
Set the factor '(7 + -6a)' equal to zero and attempt to solve:

Simplifying
7 + -6a = 0

Solving
7 + -6a = 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 + -6a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6a = 0 + -7
-6a = 0 + -7

Combine like terms: 0 + -7 = -7
-6a = -7

Divide each side by '-6'.
a = 1.166666667

Simplifying
a = 1.166666667

Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {1.166666667, 8}

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