X(X-3)-13=7-X(8-X)

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Solution for X(X-3)-13=7-X(8-X) equation: 


Simplifying
X(X + -3) + -13 = 7 + -1X(8 + -1X)

Reorder the terms:
X(-3 + X) + -13 = 7 + -1X(8 + -1X)
(-3 * X + X * X) + -13 = 7 + -1X(8 + -1X)
(-3X + X2) + -13 = 7 + -1X(8 + -1X)

Reorder the terms:
-13 + -3X + X2 = 7 + -1X(8 + -1X)
-13 + -3X + X2 = 7 + (8 * -1X + -1X * -1X)
-13 + -3X + X2 = 7 + (-8X + 1X2)

Solving
-13 + -3X + X2 = 7 + -8X + 1X2

Solving for variable 'X'.

Reorder the terms:
-13 + -7 + -3X + 8X + X2 + -1X2 = 7 + -8X + 1X2 + -7 + 8X + -1X2

Combine like terms: -13 + -7 = -20
-20 + -3X + 8X + X2 + -1X2 = 7 + -8X + 1X2 + -7 + 8X + -1X2

Combine like terms: -3X + 8X = 5X
-20 + 5X + X2 + -1X2 = 7 + -8X + 1X2 + -7 + 8X + -1X2

Combine like terms: X2 + -1X2 = 0
-20 + 5X + 0 = 7 + -8X + 1X2 + -7 + 8X + -1X2
-20 + 5X = 7 + -8X + 1X2 + -7 + 8X + -1X2

Reorder the terms:
-20 + 5X = 7 + -7 + -8X + 8X + 1X2 + -1X2

Combine like terms: 7 + -7 = 0
-20 + 5X = 0 + -8X + 8X + 1X2 + -1X2
-20 + 5X = -8X + 8X + 1X2 + -1X2

Combine like terms: -8X + 8X = 0
-20 + 5X = 0 + 1X2 + -1X2
-20 + 5X = 1X2 + -1X2

Combine like terms: 1X2 + -1X2 = 0
-20 + 5X = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + X) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-4 + X)' equal to zero and attempt to solve:

Simplifying
-4 + X = 0

Solving
-4 + X = 0

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

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

Combine like terms: -4 + 4 = 0
0 + X = 0 + 4
X = 0 + 4

Combine like terms: 0 + 4 = 4
X = 4

Simplifying
X = 4
Solution
X = {4}

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