3a^2-2a(6a+2)+(3a+2)(7a-3)=

Solution for 3a^2-2a(6a+2)+(3a+2)(7a-3)= equation:

Simplifying
3a2 + -2a(6a + 2) + (3a + 2)(7a + -3) = 0

Reorder the terms:
3a2 + -2a(2 + 6a) + (3a + 2)(7a + -3) = 0
3a2 + (2 * -2a + 6a * -2a) + (3a + 2)(7a + -3) = 0
3a2 + (-4a + -12a2) + (3a + 2)(7a + -3) = 0

Reorder the terms:
3a2 + -4a + -12a2 + (2 + 3a)(7a + -3) = 0

Reorder the terms:
3a2 + -4a + -12a2 + (2 + 3a)(-3 + 7a) = 0

Multiply (2 + 3a) * (-3 + 7a)
3a2 + -4a + -12a2 + (2(-3 + 7a) + 3a * (-3 + 7a)) = 0
3a2 + -4a + -12a2 + ((-3 * 2 + 7a * 2) + 3a * (-3 + 7a)) = 0
3a2 + -4a + -12a2 + ((-6 + 14a) + 3a * (-3 + 7a)) = 0
3a2 + -4a + -12a2 + (-6 + 14a + (-3 * 3a + 7a * 3a)) = 0
3a2 + -4a + -12a2 + (-6 + 14a + (-9a + 21a2)) = 0

Combine like terms: 14a + -9a = 5a
3a2 + -4a + -12a2 + (-6 + 5a + 21a2) = 0

Reorder the terms:
-6 + -4a + 5a + 3a2 + -12a2 + 21a2 = 0

Combine like terms: -4a + 5a = 1a
-6 + 1a + 3a2 + -12a2 + 21a2 = 0

Combine like terms: 3a2 + -12a2 = -9a2
-6 + 1a + -9a2 + 21a2 = 0

Combine like terms: -9a2 + 21a2 = 12a2
-6 + 1a + 12a2 = 0

Solving
-6 + 1a + 12a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -4a)(2 + -3a) = 0

Subproblem 1
Set the factor '(-3 + -4a)' equal to zero and attempt to solve:

Simplifying
-3 + -4a = 0

Solving
-3 + -4a = 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 + -4a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4a = 0 + 3
-4a = 0 + 3

Combine like terms: 0 + 3 = 3
-4a = 3

Divide each side by '-4'.
a = -0.75

Simplifying
a = -0.75
Subproblem 2
Set the factor '(2 + -3a)' equal to zero and attempt to solve:

Simplifying
2 + -3a = 0

Solving
2 + -3a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3a = 0 + -2
-3a = 0 + -2

Combine like terms: 0 + -2 = -2
-3a = -2

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
Solution
a = {-0.75, 0.6666666667}