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

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


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

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

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

Multiply (-1 + x) * (1 + x)
(-1(1 + x) + x(1 + x)) = 5x + 13
((1 * -1 + x * -1) + x(1 + x)) = 5x + 13
((-1 + -1x) + x(1 + x)) = 5x + 13
(-1 + -1x + (1 * x + x * x)) = 5x + 13
(-1 + -1x + (1x + x2)) = 5x + 13

Combine like terms: -1x + 1x = 0
(-1 + 0 + x2) = 5x + 13
(-1 + x2) = 5x + 13

Reorder the terms:
-1 + x2 = 13 + 5x

Solving
-1 + x2 = 13 + 5x

Solving for variable 'x'.

Reorder the terms:
-1 + -13 + -5x + x2 = 13 + 5x + -13 + -5x

Combine like terms: -1 + -13 = -14
-14 + -5x + x2 = 13 + 5x + -13 + -5x

Reorder the terms:
-14 + -5x + x2 = 13 + -13 + 5x + -5x

Combine like terms: 13 + -13 = 0
-14 + -5x + x2 = 0 + 5x + -5x
-14 + -5x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-14 + -5x + x2 = 0

Factor a trinomial.
(-2 + -1x)(7 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-2, 7}

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