13x-7=12x(x-1)+x+5

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Solution for 13x-7=12x(x-1)+x+5 equation:


Simplifying
13x + -7 = 12x(x + -1) + x + 5

Reorder the terms:
-7 + 13x = 12x(x + -1) + x + 5

Reorder the terms:
-7 + 13x = 12x(-1 + x) + x + 5
-7 + 13x = (-1 * 12x + x * 12x) + x + 5
-7 + 13x = (-12x + 12x2) + x + 5

Reorder the terms:
-7 + 13x = 5 + -12x + x + 12x2

Combine like terms: -12x + x = -11x
-7 + 13x = 5 + -11x + 12x2

Solving
-7 + 13x = 5 + -11x + 12x2

Solving for variable 'x'.

Reorder the terms:
-7 + -5 + 13x + 11x + -12x2 = 5 + -11x + 12x2 + -5 + 11x + -12x2

Combine like terms: -7 + -5 = -12
-12 + 13x + 11x + -12x2 = 5 + -11x + 12x2 + -5 + 11x + -12x2

Combine like terms: 13x + 11x = 24x
-12 + 24x + -12x2 = 5 + -11x + 12x2 + -5 + 11x + -12x2

Reorder the terms:
-12 + 24x + -12x2 = 5 + -5 + -11x + 11x + 12x2 + -12x2

Combine like terms: 5 + -5 = 0
-12 + 24x + -12x2 = 0 + -11x + 11x + 12x2 + -12x2
-12 + 24x + -12x2 = -11x + 11x + 12x2 + -12x2

Combine like terms: -11x + 11x = 0
-12 + 24x + -12x2 = 0 + 12x2 + -12x2
-12 + 24x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-12 + 24x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-1 + 2x + -1x2) = 0

Factor a trinomial.
12((-1 + x)(1 + -1x)) = 0

Ignore the factor 12.

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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

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

Simplifying
x = 1

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {1, 1}

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