7z^2+6z-3=(8z+1)(z-3)

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Solution for 7z^2+6z-3=(8z+1)(z-3) equation: 


Simplifying
7z2 + 6z + -3 = (8z + 1)(z + -3)

Reorder the terms:
-3 + 6z + 7z2 = (8z + 1)(z + -3)

Reorder the terms:
-3 + 6z + 7z2 = (1 + 8z)(z + -3)

Reorder the terms:
-3 + 6z + 7z2 = (1 + 8z)(-3 + z)

Multiply (1 + 8z) * (-3 + z)
-3 + 6z + 7z2 = (1(-3 + z) + 8z * (-3 + z))
-3 + 6z + 7z2 = ((-3 * 1 + z * 1) + 8z * (-3 + z))
-3 + 6z + 7z2 = ((-3 + 1z) + 8z * (-3 + z))
-3 + 6z + 7z2 = (-3 + 1z + (-3 * 8z + z * 8z))
-3 + 6z + 7z2 = (-3 + 1z + (-24z + 8z2))

Combine like terms: 1z + -24z = -23z
-3 + 6z + 7z2 = (-3 + -23z + 8z2)

Add '3' to each side of the equation.
-3 + 6z + 3 + 7z2 = -3 + -23z + 3 + 8z2

Reorder the terms:
-3 + 3 + 6z + 7z2 = -3 + -23z + 3 + 8z2

Combine like terms: -3 + 3 = 0
0 + 6z + 7z2 = -3 + -23z + 3 + 8z2
6z + 7z2 = -3 + -23z + 3 + 8z2

Reorder the terms:
6z + 7z2 = -3 + 3 + -23z + 8z2

Combine like terms: -3 + 3 = 0
6z + 7z2 = 0 + -23z + 8z2
6z + 7z2 = -23z + 8z2

Solving
6z + 7z2 = -23z + 8z2

Solving for variable 'z'.

Reorder the terms:
6z + 23z + 7z2 + -8z2 = -23z + 8z2 + 23z + -8z2

Combine like terms: 6z + 23z = 29z
29z + 7z2 + -8z2 = -23z + 8z2 + 23z + -8z2

Combine like terms: 7z2 + -8z2 = -1z2
29z + -1z2 = -23z + 8z2 + 23z + -8z2

Reorder the terms:
29z + -1z2 = -23z + 23z + 8z2 + -8z2

Combine like terms: -23z + 23z = 0
29z + -1z2 = 0 + 8z2 + -8z2
29z + -1z2 = 8z2 + -8z2

Combine like terms: 8z2 + -8z2 = 0
29z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(29 + -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 '(29 + -1z)' equal to zero and attempt to solve:

Simplifying
29 + -1z = 0

Solving
29 + -1z = 0

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

Add '-29' to each side of the equation.
29 + -29 + -1z = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -1z = 0 + -29
-1z = 0 + -29

Combine like terms: 0 + -29 = -29
-1z = -29

Divide each side by '-1'.
z = 29

Simplifying
z = 29
Solution
z = {0, 29}

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