x^2-x-5=5x-5

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Solution for x^2-x-5=5x-5 equation:


Simplifying
x2 + -1x + -5 = 5x + -5

Reorder the terms:
-5 + -1x + x2 = 5x + -5

Reorder the terms:
-5 + -1x + x2 = -5 + 5x

Add '5' to each side of the equation.
-5 + -1x + 5 + x2 = -5 + 5 + 5x

Reorder the terms:
-5 + 5 + -1x + x2 = -5 + 5 + 5x

Combine like terms: -5 + 5 = 0
0 + -1x + x2 = -5 + 5 + 5x
-1x + x2 = -5 + 5 + 5x

Combine like terms: -5 + 5 = 0
-1x + x2 = 0 + 5x
-1x + x2 = 5x

Solving
-1x + x2 = 5x

Solving for variable 'x'.

Reorder the terms:
-1x + -5x + x2 = 5x + -5x

Combine like terms: -1x + -5x = -6x
-6x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-6x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + x) = 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6

Solution

x = {0, 6}

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