(c+4)(c-3)+6(1+c^2)=(c-2)(c+2)

Solution for (c+4)(c-3)+6(1+c^2)=(c-2)(c+2) equation:

Simplifying
(c + 4)(c + -3) + 6(1 + c2) = (c + -2)(c + 2)

Reorder the terms:
(4 + c)(c + -3) + 6(1 + c2) = (c + -2)(c + 2)

Reorder the terms:
(4 + c)(-3 + c) + 6(1 + c2) = (c + -2)(c + 2)

Multiply (4 + c) * (-3 + c)
(4(-3 + c) + c(-3 + c)) + 6(1 + c2) = (c + -2)(c + 2)
((-3 * 4 + c * 4) + c(-3 + c)) + 6(1 + c2) = (c + -2)(c + 2)
((-12 + 4c) + c(-3 + c)) + 6(1 + c2) = (c + -2)(c + 2)
(-12 + 4c + (-3 * c + c * c)) + 6(1 + c2) = (c + -2)(c + 2)
(-12 + 4c + (-3c + c2)) + 6(1 + c2) = (c + -2)(c + 2)

Combine like terms: 4c + -3c = 1c
(-12 + 1c + c2) + 6(1 + c2) = (c + -2)(c + 2)
-12 + 1c + c2 + (1 * 6 + c2 * 6) = (c + -2)(c + 2)
-12 + 1c + c2 + (6 + 6c2) = (c + -2)(c + 2)

Reorder the terms:
-12 + 6 + 1c + c2 + 6c2 = (c + -2)(c + 2)

Combine like terms: -12 + 6 = -6
-6 + 1c + c2 + 6c2 = (c + -2)(c + 2)

Combine like terms: c2 + 6c2 = 7c2
-6 + 1c + 7c2 = (c + -2)(c + 2)

Reorder the terms:
-6 + 1c + 7c2 = (-2 + c)(c + 2)

Reorder the terms:
-6 + 1c + 7c2 = (-2 + c)(2 + c)

Multiply (-2 + c) * (2 + c)
-6 + 1c + 7c2 = (-2(2 + c) + c(2 + c))
-6 + 1c + 7c2 = ((2 * -2 + c * -2) + c(2 + c))
-6 + 1c + 7c2 = ((-4 + -2c) + c(2 + c))
-6 + 1c + 7c2 = (-4 + -2c + (2 * c + c * c))
-6 + 1c + 7c2 = (-4 + -2c + (2c + c2))

Combine like terms: -2c + 2c = 0
-6 + 1c + 7c2 = (-4 + 0 + c2)
-6 + 1c + 7c2 = (-4 + c2)

Solving
-6 + 1c + 7c2 = -4 + c2

Solving for variable 'c'.

Reorder the terms:
-6 + 4 + 1c + 7c2 + -1c2 = -4 + c2 + 4 + -1c2

Combine like terms: -6 + 4 = -2
-2 + 1c + 7c2 + -1c2 = -4 + c2 + 4 + -1c2

Combine like terms: 7c2 + -1c2 = 6c2
-2 + 1c + 6c2 = -4 + c2 + 4 + -1c2

Reorder the terms:
-2 + 1c + 6c2 = -4 + 4 + c2 + -1c2

Combine like terms: -4 + 4 = 0
-2 + 1c + 6c2 = 0 + c2 + -1c2
-2 + 1c + 6c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
-2 + 1c + 6c2 = 0

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

Subproblem 1
Set the factor '(-2 + -3c)' equal to zero and attempt to solve:

Simplifying
-2 + -3c = 0

Solving
-2 + -3c = 0

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

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

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

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

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

Simplifying
c = -0.6666666667
Subproblem 2
Set the factor '(1 + -2c)' equal to zero and attempt to solve:

Simplifying
1 + -2c = 0

Solving
1 + -2c = 0

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

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

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

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

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

Simplifying
c = 0.5
Solution
c = {-0.6666666667, 0.5}