(x+6)(x-1)=(2x+1)(x-1)

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Solution for (x+6)(x-1)=(2x+1)(x-1) equation:


Simplifying
(x + 6)(x + -1) = (2x + 1)(x + -1)

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

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

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

Combine like terms: 6x + -1x = 5x
(-6 + 5x + x2) = (2x + 1)(x + -1)

Reorder the terms:
-6 + 5x + x2 = (1 + 2x)(x + -1)

Reorder the terms:
-6 + 5x + x2 = (1 + 2x)(-1 + x)

Multiply (1 + 2x) * (-1 + x)
-6 + 5x + x2 = (1(-1 + x) + 2x * (-1 + x))
-6 + 5x + x2 = ((-1 * 1 + x * 1) + 2x * (-1 + x))
-6 + 5x + x2 = ((-1 + 1x) + 2x * (-1 + x))
-6 + 5x + x2 = (-1 + 1x + (-1 * 2x + x * 2x))
-6 + 5x + x2 = (-1 + 1x + (-2x + 2x2))

Combine like terms: 1x + -2x = -1x
-6 + 5x + x2 = (-1 + -1x + 2x2)

Solving
-6 + 5x + x2 = -1 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-6 + 1 + 5x + x + x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2

Combine like terms: -6 + 1 = -5
-5 + 5x + x + x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2

Combine like terms: 5x + x = 6x
-5 + 6x + x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-5 + 6x + -1x2 = -1 + -1x + 2x2 + 1 + x + -2x2

Reorder the terms:
-5 + 6x + -1x2 = -1 + 1 + -1x + x + 2x2 + -2x2

Combine like terms: -1 + 1 = 0
-5 + 6x + -1x2 = 0 + -1x + x + 2x2 + -2x2
-5 + 6x + -1x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-5 + 6x + -1x2 = 0 + 2x2 + -2x2
-5 + 6x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + 6x + -1x2 = 0

Factor a trinomial.
(-5 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

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

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

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 = {5, 1}

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