(g+3)(2-g)=g^2

Solution for (g+3)(2-g)=g^2 equation:

Simplifying
(g + 3)(2 + -1g) = g2

Reorder the terms:
(3 + g)(2 + -1g) = g2

Multiply (3 + g) * (2 + -1g)
(3(2 + -1g) + g(2 + -1g)) = g2
((2 * 3 + -1g * 3) + g(2 + -1g)) = g2
((6 + -3g) + g(2 + -1g)) = g2
(6 + -3g + (2 * g + -1g * g)) = g2
(6 + -3g + (2g + -1g2)) = g2

Combine like terms: -3g + 2g = -1g
(6 + -1g + -1g2) = g2

Solving
6 + -1g + -1g2 = g2

Solving for variable 'g'.

Combine like terms: -1g2 + -1g2 = -2g2
6 + -1g + -2g2 = g2 + -1g2

Combine like terms: g2 + -1g2 = 0
6 + -1g + -2g2 = 0

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

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

Simplifying
3 + -2g = 0

Solving
3 + -2g = 0

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

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

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

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

Divide each side by '-2'.
g = 1.5

Simplifying
g = 1.5
Subproblem 2
Set the factor '(2 + g)' equal to zero and attempt to solve:

Simplifying
2 + g = 0

Solving
2 + g = 0

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

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

Combine like terms: 2 + -2 = 0
0 + g = 0 + -2
g = 0 + -2

Combine like terms: 0 + -2 = -2
g = -2

Simplifying
g = -2
Solution
g = {1.5, -2}