z^2+3z-15=(2z+5)(z-3)

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Solution for z^2+3z-15=(2z+5)(z-3) equation: 


Simplifying
z2 + 3z + -15 = (2z + 5)(z + -3)

Reorder the terms:
-15 + 3z + z2 = (2z + 5)(z + -3)

Reorder the terms:
-15 + 3z + z2 = (5 + 2z)(z + -3)

Reorder the terms:
-15 + 3z + z2 = (5 + 2z)(-3 + z)

Multiply (5 + 2z) * (-3 + z)
-15 + 3z + z2 = (5(-3 + z) + 2z * (-3 + z))
-15 + 3z + z2 = ((-3 * 5 + z * 5) + 2z * (-3 + z))
-15 + 3z + z2 = ((-15 + 5z) + 2z * (-3 + z))
-15 + 3z + z2 = (-15 + 5z + (-3 * 2z + z * 2z))
-15 + 3z + z2 = (-15 + 5z + (-6z + 2z2))

Combine like terms: 5z + -6z = -1z
-15 + 3z + z2 = (-15 + -1z + 2z2)

Add '15' to each side of the equation.
-15 + 3z + 15 + z2 = -15 + -1z + 15 + 2z2

Reorder the terms:
-15 + 15 + 3z + z2 = -15 + -1z + 15 + 2z2

Combine like terms: -15 + 15 = 0
0 + 3z + z2 = -15 + -1z + 15 + 2z2
3z + z2 = -15 + -1z + 15 + 2z2

Reorder the terms:
3z + z2 = -15 + 15 + -1z + 2z2

Combine like terms: -15 + 15 = 0
3z + z2 = 0 + -1z + 2z2
3z + z2 = -1z + 2z2

Solving
3z + z2 = -1z + 2z2

Solving for variable 'z'.

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

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

Combine like terms: z2 + -2z2 = -1z2
4z + -1z2 = -1z + 2z2 + z + -2z2

Reorder the terms:
4z + -1z2 = -1z + z + 2z2 + -2z2

Combine like terms: -1z + z = 0
4z + -1z2 = 0 + 2z2 + -2z2
4z + -1z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
4z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(4 + -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 '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {0, 4}

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