z^2+9z-63=(2z+7)(z-9)

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Solution for z^2+9z-63=(2z+7)(z-9) equation: 


Simplifying
z2 + 9z + -63 = (2z + 7)(z + -9)

Reorder the terms:
-63 + 9z + z2 = (2z + 7)(z + -9)

Reorder the terms:
-63 + 9z + z2 = (7 + 2z)(z + -9)

Reorder the terms:
-63 + 9z + z2 = (7 + 2z)(-9 + z)

Multiply (7 + 2z) * (-9 + z)
-63 + 9z + z2 = (7(-9 + z) + 2z * (-9 + z))
-63 + 9z + z2 = ((-9 * 7 + z * 7) + 2z * (-9 + z))
-63 + 9z + z2 = ((-63 + 7z) + 2z * (-9 + z))
-63 + 9z + z2 = (-63 + 7z + (-9 * 2z + z * 2z))
-63 + 9z + z2 = (-63 + 7z + (-18z + 2z2))

Combine like terms: 7z + -18z = -11z
-63 + 9z + z2 = (-63 + -11z + 2z2)

Add '63' to each side of the equation.
-63 + 9z + 63 + z2 = -63 + -11z + 63 + 2z2

Reorder the terms:
-63 + 63 + 9z + z2 = -63 + -11z + 63 + 2z2

Combine like terms: -63 + 63 = 0
0 + 9z + z2 = -63 + -11z + 63 + 2z2
9z + z2 = -63 + -11z + 63 + 2z2

Reorder the terms:
9z + z2 = -63 + 63 + -11z + 2z2

Combine like terms: -63 + 63 = 0
9z + z2 = 0 + -11z + 2z2
9z + z2 = -11z + 2z2

Solving
9z + z2 = -11z + 2z2

Solving for variable 'z'.

Reorder the terms:
9z + 11z + z2 + -2z2 = -11z + 2z2 + 11z + -2z2

Combine like terms: 9z + 11z = 20z
20z + z2 + -2z2 = -11z + 2z2 + 11z + -2z2

Combine like terms: z2 + -2z2 = -1z2
20z + -1z2 = -11z + 2z2 + 11z + -2z2

Reorder the terms:
20z + -1z2 = -11z + 11z + 2z2 + -2z2

Combine like terms: -11z + 11z = 0
20z + -1z2 = 0 + 2z2 + -2z2
20z + -1z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
20z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(20 + -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 '(20 + -1z)' equal to zero and attempt to solve:

Simplifying
20 + -1z = 0

Solving
20 + -1z = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1z = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1z = 0 + -20
-1z = 0 + -20

Combine like terms: 0 + -20 = -20
-1z = -20

Divide each side by '-1'.
z = 20

Simplifying
z = 20
Solution
z = {0, 20}

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