x^2-12x+6=5x+6

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Solution for x^2-12x+6=5x+6 equation:


Simplifying
x2 + -12x + 6 = 5x + 6

Reorder the terms:
6 + -12x + x2 = 5x + 6

Reorder the terms:
6 + -12x + x2 = 6 + 5x

Add '-6' to each side of the equation.
6 + -12x + -6 + x2 = 6 + -6 + 5x

Reorder the terms:
6 + -6 + -12x + x2 = 6 + -6 + 5x

Combine like terms: 6 + -6 = 0
0 + -12x + x2 = 6 + -6 + 5x
-12x + x2 = 6 + -6 + 5x

Combine like terms: 6 + -6 = 0
-12x + x2 = 0 + 5x
-12x + x2 = 5x

Solving
-12x + x2 = 5x

Solving for variable 'x'.

Reorder the terms:
-12x + -5x + x2 = 5x + -5x

Combine like terms: -12x + -5x = -17x
-17x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-17x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-17 + 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 '(-17 + x)' equal to zero and attempt to solve: Simplifying -17 + x = 0 Solving -17 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + x = 0 + 17 x = 0 + 17 Combine like terms: 0 + 17 = 17 x = 17 Simplifying x = 17

Solution

x = {0, 17}

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