5-z=3-(z+2)(z-2)

Solution for 5-z=3-(z+2)(z-2) equation:

Simplifying
5 + -1z = 3 + -1(z + 2)(z + -2)

Reorder the terms:
5 + -1z = 3 + -1(2 + z)(z + -2)

Reorder the terms:
5 + -1z = 3 + -1(2 + z)(-2 + z)

Multiply (2 + z) * (-2 + z)
5 + -1z = 3 + -1(2(-2 + z) + z(-2 + z))
5 + -1z = 3 + -1((-2 * 2 + z * 2) + z(-2 + z))
5 + -1z = 3 + -1((-4 + 2z) + z(-2 + z))
5 + -1z = 3 + -1(-4 + 2z + (-2 * z + z * z))
5 + -1z = 3 + -1(-4 + 2z + (-2z + z2))

Combine like terms: 2z + -2z = 0
5 + -1z = 3 + -1(-4 + 0 + z2)
5 + -1z = 3 + -1(-4 + z2)
5 + -1z = 3 + (-4 * -1 + z2 * -1)
5 + -1z = 3 + (4 + -1z2)

Combine like terms: 3 + 4 = 7
5 + -1z = 7 + -1z2

Solving
5 + -1z = 7 + -1z2

Solving for variable 'z'.

Reorder the terms:
5 + -7 + -1z + z2 = 7 + -1z2 + -7 + z2

Combine like terms: 5 + -7 = -2
-2 + -1z + z2 = 7 + -1z2 + -7 + z2

Reorder the terms:
-2 + -1z + z2 = 7 + -7 + -1z2 + z2

Combine like terms: 7 + -7 = 0
-2 + -1z + z2 = 0 + -1z2 + z2
-2 + -1z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-2 + -1z + z2 = 0

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

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

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1z = 0 + 1
-1z = 0 + 1

Combine like terms: 0 + 1 = 1
-1z = 1

Divide each side by '-1'.
z = -1

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

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

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-1, 2}