(x+1)(x-7)=(2x+1)(x-7)

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Solution for (x+1)(x-7)=(2x+1)(x-7) equation: 


Simplifying
(x + 1)(x + -7) = (2x + 1)(x + -7)

Reorder the terms:
(1 + x)(x + -7) = (2x + 1)(x + -7)

Reorder the terms:
(1 + x)(-7 + x) = (2x + 1)(x + -7)

Multiply (1 + x) * (-7 + x)
(1(-7 + x) + x(-7 + x)) = (2x + 1)(x + -7)
((-7 * 1 + x * 1) + x(-7 + x)) = (2x + 1)(x + -7)
((-7 + 1x) + x(-7 + x)) = (2x + 1)(x + -7)
(-7 + 1x + (-7 * x + x * x)) = (2x + 1)(x + -7)
(-7 + 1x + (-7x + x2)) = (2x + 1)(x + -7)

Combine like terms: 1x + -7x = -6x
(-7 + -6x + x2) = (2x + 1)(x + -7)

Reorder the terms:
-7 + -6x + x2 = (1 + 2x)(x + -7)

Reorder the terms:
-7 + -6x + x2 = (1 + 2x)(-7 + x)

Multiply (1 + 2x) * (-7 + x)
-7 + -6x + x2 = (1(-7 + x) + 2x * (-7 + x))
-7 + -6x + x2 = ((-7 * 1 + x * 1) + 2x * (-7 + x))
-7 + -6x + x2 = ((-7 + 1x) + 2x * (-7 + x))
-7 + -6x + x2 = (-7 + 1x + (-7 * 2x + x * 2x))
-7 + -6x + x2 = (-7 + 1x + (-14x + 2x2))

Combine like terms: 1x + -14x = -13x
-7 + -6x + x2 = (-7 + -13x + 2x2)

Add '7' to each side of the equation.
-7 + -6x + 7 + x2 = -7 + -13x + 7 + 2x2

Reorder the terms:
-7 + 7 + -6x + x2 = -7 + -13x + 7 + 2x2

Combine like terms: -7 + 7 = 0
0 + -6x + x2 = -7 + -13x + 7 + 2x2
-6x + x2 = -7 + -13x + 7 + 2x2

Reorder the terms:
-6x + x2 = -7 + 7 + -13x + 2x2

Combine like terms: -7 + 7 = 0
-6x + x2 = 0 + -13x + 2x2
-6x + x2 = -13x + 2x2

Solving
-6x + x2 = -13x + 2x2

Solving for variable 'x'.

Reorder the terms:
-6x + 13x + x2 + -2x2 = -13x + 2x2 + 13x + -2x2

Combine like terms: -6x + 13x = 7x
7x + x2 + -2x2 = -13x + 2x2 + 13x + -2x2

Combine like terms: x2 + -2x2 = -1x2
7x + -1x2 = -13x + 2x2 + 13x + -2x2

Reorder the terms:
7x + -1x2 = -13x + 13x + 2x2 + -2x2

Combine like terms: -13x + 13x = 0
7x + -1x2 = 0 + 2x2 + -2x2
7x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + -1x) = 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 '(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 = {0, 7}

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