5z^2+7z-5=(6z+1)(z-5)

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Solution for 5z^2+7z-5=(6z+1)(z-5) equation: 


Simplifying
5z2 + 7z + -5 = (6z + 1)(z + -5)

Reorder the terms:
-5 + 7z + 5z2 = (6z + 1)(z + -5)

Reorder the terms:
-5 + 7z + 5z2 = (1 + 6z)(z + -5)

Reorder the terms:
-5 + 7z + 5z2 = (1 + 6z)(-5 + z)

Multiply (1 + 6z) * (-5 + z)
-5 + 7z + 5z2 = (1(-5 + z) + 6z * (-5 + z))
-5 + 7z + 5z2 = ((-5 * 1 + z * 1) + 6z * (-5 + z))
-5 + 7z + 5z2 = ((-5 + 1z) + 6z * (-5 + z))
-5 + 7z + 5z2 = (-5 + 1z + (-5 * 6z + z * 6z))
-5 + 7z + 5z2 = (-5 + 1z + (-30z + 6z2))

Combine like terms: 1z + -30z = -29z
-5 + 7z + 5z2 = (-5 + -29z + 6z2)

Add '5' to each side of the equation.
-5 + 7z + 5 + 5z2 = -5 + -29z + 5 + 6z2

Reorder the terms:
-5 + 5 + 7z + 5z2 = -5 + -29z + 5 + 6z2

Combine like terms: -5 + 5 = 0
0 + 7z + 5z2 = -5 + -29z + 5 + 6z2
7z + 5z2 = -5 + -29z + 5 + 6z2

Reorder the terms:
7z + 5z2 = -5 + 5 + -29z + 6z2

Combine like terms: -5 + 5 = 0
7z + 5z2 = 0 + -29z + 6z2
7z + 5z2 = -29z + 6z2

Solving
7z + 5z2 = -29z + 6z2

Solving for variable 'z'.

Reorder the terms:
7z + 29z + 5z2 + -6z2 = -29z + 6z2 + 29z + -6z2

Combine like terms: 7z + 29z = 36z
36z + 5z2 + -6z2 = -29z + 6z2 + 29z + -6z2

Combine like terms: 5z2 + -6z2 = -1z2
36z + -1z2 = -29z + 6z2 + 29z + -6z2

Reorder the terms:
36z + -1z2 = -29z + 29z + 6z2 + -6z2

Combine like terms: -29z + 29z = 0
36z + -1z2 = 0 + 6z2 + -6z2
36z + -1z2 = 6z2 + -6z2

Combine like terms: 6z2 + -6z2 = 0
36z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(36 + -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 '(36 + -1z)' equal to zero and attempt to solve:

Simplifying
36 + -1z = 0

Solving
36 + -1z = 0

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

Add '-36' to each side of the equation.
36 + -36 + -1z = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -1z = 0 + -36
-1z = 0 + -36

Combine like terms: 0 + -36 = -36
-1z = -36

Divide each side by '-1'.
z = 36

Simplifying
z = 36
Solution
z = {0, 36}

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