(x+7)(x-1)=(2x+3)(x-1)

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Solution for (x+7)(x-1)=(2x+3)(x-1) equation: 


Simplifying
(x + 7)(x + -1) = (2x + 3)(x + -1)

Reorder the terms:
(7 + x)(x + -1) = (2x + 3)(x + -1)

Reorder the terms:
(7 + x)(-1 + x) = (2x + 3)(x + -1)

Multiply (7 + x) * (-1 + x)
(7(-1 + x) + x(-1 + x)) = (2x + 3)(x + -1)
((-1 * 7 + x * 7) + x(-1 + x)) = (2x + 3)(x + -1)
((-7 + 7x) + x(-1 + x)) = (2x + 3)(x + -1)
(-7 + 7x + (-1 * x + x * x)) = (2x + 3)(x + -1)
(-7 + 7x + (-1x + x2)) = (2x + 3)(x + -1)

Combine like terms: 7x + -1x = 6x
(-7 + 6x + x2) = (2x + 3)(x + -1)

Reorder the terms:
-7 + 6x + x2 = (3 + 2x)(x + -1)

Reorder the terms:
-7 + 6x + x2 = (3 + 2x)(-1 + x)

Multiply (3 + 2x) * (-1 + x)
-7 + 6x + x2 = (3(-1 + x) + 2x * (-1 + x))
-7 + 6x + x2 = ((-1 * 3 + x * 3) + 2x * (-1 + x))
-7 + 6x + x2 = ((-3 + 3x) + 2x * (-1 + x))
-7 + 6x + x2 = (-3 + 3x + (-1 * 2x + x * 2x))
-7 + 6x + x2 = (-3 + 3x + (-2x + 2x2))

Combine like terms: 3x + -2x = 1x
-7 + 6x + x2 = (-3 + 1x + 2x2)

Solving
-7 + 6x + x2 = -3 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-7 + 3 + 6x + -1x + x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Combine like terms: -7 + 3 = -4
-4 + 6x + -1x + x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Combine like terms: 6x + -1x = 5x
-4 + 5x + x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-4 + 5x + -1x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Reorder the terms:
-4 + 5x + -1x2 = -3 + 3 + 1x + -1x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
-4 + 5x + -1x2 = 0 + 1x + -1x + 2x2 + -2x2
-4 + 5x + -1x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
-4 + 5x + -1x2 = 0 + 2x2 + -2x2
-4 + 5x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + 5x + -1x2 = 0

Factor a trinomial.
(-4 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

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 = {4, 1}

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