z^2+2z-54=(2z+9)(z-6)

Solution for z^2+2z-54=(2z+9)(z-6) equation:

Simplifying
z2 + 2z + -54 = (2z + 9)(z + -6)

Reorder the terms:
-54 + 2z + z2 = (2z + 9)(z + -6)

Reorder the terms:
-54 + 2z + z2 = (9 + 2z)(z + -6)

Reorder the terms:
-54 + 2z + z2 = (9 + 2z)(-6 + z)

Multiply (9 + 2z) * (-6 + z)
-54 + 2z + z2 = (9(-6 + z) + 2z * (-6 + z))
-54 + 2z + z2 = ((-6 * 9 + z * 9) + 2z * (-6 + z))
-54 + 2z + z2 = ((-54 + 9z) + 2z * (-6 + z))
-54 + 2z + z2 = (-54 + 9z + (-6 * 2z + z * 2z))
-54 + 2z + z2 = (-54 + 9z + (-12z + 2z2))

Combine like terms: 9z + -12z = -3z
-54 + 2z + z2 = (-54 + -3z + 2z2)

Add '54' to each side of the equation.
-54 + 2z + 54 + z2 = -54 + -3z + 54 + 2z2

Reorder the terms:
-54 + 54 + 2z + z2 = -54 + -3z + 54 + 2z2

Combine like terms: -54 + 54 = 0
0 + 2z + z2 = -54 + -3z + 54 + 2z2
2z + z2 = -54 + -3z + 54 + 2z2

Reorder the terms:
2z + z2 = -54 + 54 + -3z + 2z2

Combine like terms: -54 + 54 = 0
2z + z2 = 0 + -3z + 2z2
2z + z2 = -3z + 2z2

Solving
2z + z2 = -3z + 2z2

Solving for variable 'z'.

Reorder the terms:
2z + 3z + z2 + -2z2 = -3z + 2z2 + 3z + -2z2

Combine like terms: 2z + 3z = 5z
5z + z2 + -2z2 = -3z + 2z2 + 3z + -2z2

Combine like terms: z2 + -2z2 = -1z2
5z + -1z2 = -3z + 2z2 + 3z + -2z2

Reorder the terms:
5z + -1z2 = -3z + 3z + 2z2 + -2z2

Combine like terms: -3z + 3z = 0
5z + -1z2 = 0 + 2z2 + -2z2
5z + -1z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
5z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(5 + -1z) = 0

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {0, 5}