15=(x-5)*(x-3)

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Solution for 15=(x-5)*(x-3) equation: 


Simplifying
15 = (x + -5)(x + -3)

Reorder the terms:
15 = (-5 + x)(x + -3)

Reorder the terms:
15 = (-5 + x)(-3 + x)

Multiply (-5 + x) * (-3 + x)
15 = (-5(-3 + x) + x(-3 + x))
15 = ((-3 * -5 + x * -5) + x(-3 + x))
15 = ((15 + -5x) + x(-3 + x))
15 = (15 + -5x + (-3 * x + x * x))
15 = (15 + -5x + (-3x + x2))

Combine like terms: -5x + -3x = -8x
15 = (15 + -8x + x2)

Add '-15' to each side of the equation.
15 + -15 = 15 + -8x + -15 + x2

Combine like terms: 15 + -15 = 0
0 = 15 + -8x + -15 + x2

Reorder the terms:
0 = 15 + -15 + -8x + x2

Combine like terms: 15 + -15 = 0
0 = 0 + -8x + x2
0 = -8x + x2

Solving
0 = -8x + x2

Solving for variable 'x'.
Remove the zero:
8x + -1x2 = -8x + x2 + 8x + -1x2

Reorder the terms:
8x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
8x + -1x2 = 0 + x2 + -1x2
8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + -1x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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