z^2+7z-2=(2z+1)(z-2)

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Solution for z^2+7z-2=(2z+1)(z-2) equation: 


Simplifying
z2 + 7z + -2 = (2z + 1)(z + -2)

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

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

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

Multiply (1 + 2z) * (-2 + z)
-2 + 7z + z2 = (1(-2 + z) + 2z * (-2 + z))
-2 + 7z + z2 = ((-2 * 1 + z * 1) + 2z * (-2 + z))
-2 + 7z + z2 = ((-2 + 1z) + 2z * (-2 + z))
-2 + 7z + z2 = (-2 + 1z + (-2 * 2z + z * 2z))
-2 + 7z + z2 = (-2 + 1z + (-4z + 2z2))

Combine like terms: 1z + -4z = -3z
-2 + 7z + z2 = (-2 + -3z + 2z2)

Add '2' to each side of the equation.
-2 + 7z + 2 + z2 = -2 + -3z + 2 + 2z2

Reorder the terms:
-2 + 2 + 7z + z2 = -2 + -3z + 2 + 2z2

Combine like terms: -2 + 2 = 0
0 + 7z + z2 = -2 + -3z + 2 + 2z2
7z + z2 = -2 + -3z + 2 + 2z2

Reorder the terms:
7z + z2 = -2 + 2 + -3z + 2z2

Combine like terms: -2 + 2 = 0
7z + z2 = 0 + -3z + 2z2
7z + z2 = -3z + 2z2

Solving
7z + z2 = -3z + 2z2

Solving for variable 'z'.

Reorder the terms:
7z + 3z + z2 + -2z2 = -3z + 2z2 + 3z + -2z2

Combine like terms: 7z + 3z = 10z
10z + z2 + -2z2 = -3z + 2z2 + 3z + -2z2

Combine like terms: z2 + -2z2 = -1z2
10z + -1z2 = -3z + 2z2 + 3z + -2z2

Reorder the terms:
10z + -1z2 = -3z + 3z + 2z2 + -2z2

Combine like terms: -3z + 3z = 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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