(x+7)(x-1)=(2x+9)(x-1)

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Solution for (x+7)(x-1)=(2x+9)(x-1) equation: 


Simplifying
(x + 7)(x + -1) = (2x + 9)(x + -1)

Reorder the terms:
(7 + x)(x + -1) = (2x + 9)(x + -1)

Reorder the terms:
(7 + x)(-1 + x) = (2x + 9)(x + -1)

Multiply (7 + x) * (-1 + x)
(7(-1 + x) + x(-1 + x)) = (2x + 9)(x + -1)
((-1 * 7 + x * 7) + x(-1 + x)) = (2x + 9)(x + -1)
((-7 + 7x) + x(-1 + x)) = (2x + 9)(x + -1)
(-7 + 7x + (-1 * x + x * x)) = (2x + 9)(x + -1)
(-7 + 7x + (-1x + x2)) = (2x + 9)(x + -1)

Combine like terms: 7x + -1x = 6x
(-7 + 6x + x2) = (2x + 9)(x + -1)

Reorder the terms:
-7 + 6x + x2 = (9 + 2x)(x + -1)

Reorder the terms:
-7 + 6x + x2 = (9 + 2x)(-1 + x)

Multiply (9 + 2x) * (-1 + x)
-7 + 6x + x2 = (9(-1 + x) + 2x * (-1 + x))
-7 + 6x + x2 = ((-1 * 9 + x * 9) + 2x * (-1 + x))
-7 + 6x + x2 = ((-9 + 9x) + 2x * (-1 + x))
-7 + 6x + x2 = (-9 + 9x + (-1 * 2x + x * 2x))
-7 + 6x + x2 = (-9 + 9x + (-2x + 2x2))

Combine like terms: 9x + -2x = 7x
-7 + 6x + x2 = (-9 + 7x + 2x2)

Solving
-7 + 6x + x2 = -9 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-7 + 9 + 6x + -7x + x2 + -2x2 = -9 + 7x + 2x2 + 9 + -7x + -2x2

Combine like terms: -7 + 9 = 2
2 + 6x + -7x + x2 + -2x2 = -9 + 7x + 2x2 + 9 + -7x + -2x2

Combine like terms: 6x + -7x = -1x
2 + -1x + x2 + -2x2 = -9 + 7x + 2x2 + 9 + -7x + -2x2

Combine like terms: x2 + -2x2 = -1x2
2 + -1x + -1x2 = -9 + 7x + 2x2 + 9 + -7x + -2x2

Reorder the terms:
2 + -1x + -1x2 = -9 + 9 + 7x + -7x + 2x2 + -2x2

Combine like terms: -9 + 9 = 0
2 + -1x + -1x2 = 0 + 7x + -7x + 2x2 + -2x2
2 + -1x + -1x2 = 7x + -7x + 2x2 + -2x2

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

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

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


Subproblem 1
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

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {1, -2}

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