(11a+5)(6a-7)=0

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Solution for (11a+5)(6a-7)=0 equation: 


Simplifying
(11a + 5)(6a + -7) = 0

Reorder the terms:
(5 + 11a)(6a + -7) = 0

Reorder the terms:
(5 + 11a)(-7 + 6a) = 0

Multiply (5 + 11a) * (-7 + 6a)
(5(-7 + 6a) + 11a * (-7 + 6a)) = 0
((-7 * 5 + 6a * 5) + 11a * (-7 + 6a)) = 0
((-35 + 30a) + 11a * (-7 + 6a)) = 0
(-35 + 30a + (-7 * 11a + 6a * 11a)) = 0
(-35 + 30a + (-77a + 66a2)) = 0

Combine like terms: 30a + -77a = -47a
(-35 + -47a + 66a2) = 0

Solving
-35 + -47a + 66a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -11a)(7 + -6a) = 0


Subproblem 1
Set the factor '(-5 + -11a)' equal to zero and attempt to solve:

Simplifying
-5 + -11a = 0

Solving
-5 + -11a = 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 + -11a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -11a = 0 + 5
-11a = 0 + 5

Combine like terms: 0 + 5 = 5
-11a = 5

Divide each side by '-11'.
a = -0.4545454545

Simplifying
a = -0.4545454545

Subproblem 2
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
Solution
a = {-0.4545454545, 1.166666667}

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