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

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

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

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

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

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

Combine like terms: -18a + 7a = -11a
(-21 + -11a + 6a2) = 0

Solving
-21 + -11a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -6a)(3 + -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 '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-1.166666667, 3}