z^2+5z-63=(2z+9)(z-7)

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Solution for z^2+5z-63=(2z+9)(z-7) equation: 


Simplifying
z2 + 5z + -63 = (2z + 9)(z + -7)

Reorder the terms:
-63 + 5z + z2 = (2z + 9)(z + -7)

Reorder the terms:
-63 + 5z + z2 = (9 + 2z)(z + -7)

Reorder the terms:
-63 + 5z + z2 = (9 + 2z)(-7 + z)

Multiply (9 + 2z) * (-7 + z)
-63 + 5z + z2 = (9(-7 + z) + 2z * (-7 + z))
-63 + 5z + z2 = ((-7 * 9 + z * 9) + 2z * (-7 + z))
-63 + 5z + z2 = ((-63 + 9z) + 2z * (-7 + z))
-63 + 5z + z2 = (-63 + 9z + (-7 * 2z + z * 2z))
-63 + 5z + z2 = (-63 + 9z + (-14z + 2z2))

Combine like terms: 9z + -14z = -5z
-63 + 5z + z2 = (-63 + -5z + 2z2)

Add '63' to each side of the equation.
-63 + 5z + 63 + z2 = -63 + -5z + 63 + 2z2

Reorder the terms:
-63 + 63 + 5z + z2 = -63 + -5z + 63 + 2z2

Combine like terms: -63 + 63 = 0
0 + 5z + z2 = -63 + -5z + 63 + 2z2
5z + z2 = -63 + -5z + 63 + 2z2

Reorder the terms:
5z + z2 = -63 + 63 + -5z + 2z2

Combine like terms: -63 + 63 = 0
5z + z2 = 0 + -5z + 2z2
5z + z2 = -5z + 2z2

Solving
5z + z2 = -5z + 2z2

Solving for variable 'z'.

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

Combine like terms: 5z + 5z = 10z
10z + z2 + -2z2 = -5z + 2z2 + 5z + -2z2

Combine like terms: z2 + -2z2 = -1z2
10z + -1z2 = -5z + 2z2 + 5z + -2z2

Reorder the terms:
10z + -1z2 = -5z + 5z + 2z2 + -2z2

Combine like terms: -5z + 5z = 0
10z + -1z2 = 0 + 2z2 + -2z2
10z + -1z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
10z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(10 + -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 '(10 + -1z)' equal to zero and attempt to solve:

Simplifying
10 + -1z = 0

Solving
10 + -1z = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1z = 0 + -10
-1z = 0 + -10

Combine like terms: 0 + -10 = -10
-1z = -10

Divide each side by '-1'.
z = 10

Simplifying
z = 10
Solution
z = {0, 10}

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