(6a+7)(6a-3)=

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Solution for (6a+7)(6a-3)= equation: 


Simplifying
(6a + 7)(6a + -3) = 0

Reorder the terms:
(7 + 6a)(6a + -3) = 0

Reorder the terms:
(7 + 6a)(-3 + 6a) = 0

Multiply (7 + 6a) * (-3 + 6a)
(7(-3 + 6a) + 6a * (-3 + 6a)) = 0
((-3 * 7 + 6a * 7) + 6a * (-3 + 6a)) = 0
((-21 + 42a) + 6a * (-3 + 6a)) = 0
(-21 + 42a + (-3 * 6a + 6a * 6a)) = 0
(-21 + 42a + (-18a + 36a2)) = 0

Combine like terms: 42a + -18a = 24a
(-21 + 24a + 36a2) = 0

Solving
-21 + 24a + 36a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 8a + 12a2) = 0

Factor a trinomial.
3((-7 + -6a)(1 + -2a)) = 0

Ignore the factor 3.

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 '(1 + -2a)' equal to zero and attempt to solve:

Simplifying
1 + -2a = 0

Solving
1 + -2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a = 0 + -1
-2a = 0 + -1

Combine like terms: 0 + -1 = -1
-2a = -1

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Solution
a = {-1.166666667, 0.5}

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