(x+1)*(2x+6)=(-5x+7)*(x+1)

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Solution for (x+1)*(2x+6)=(-5x+7)*(x+1) equation: 


Simplifying
(x + 1)(2x + 6) = (-5x + 7)(x + 1)

Reorder the terms:
(1 + x)(2x + 6) = (-5x + 7)(x + 1)

Reorder the terms:
(1 + x)(6 + 2x) = (-5x + 7)(x + 1)

Multiply (1 + x) * (6 + 2x)
(1(6 + 2x) + x(6 + 2x)) = (-5x + 7)(x + 1)
((6 * 1 + 2x * 1) + x(6 + 2x)) = (-5x + 7)(x + 1)
((6 + 2x) + x(6 + 2x)) = (-5x + 7)(x + 1)
(6 + 2x + (6 * x + 2x * x)) = (-5x + 7)(x + 1)
(6 + 2x + (6x + 2x2)) = (-5x + 7)(x + 1)

Combine like terms: 2x + 6x = 8x
(6 + 8x + 2x2) = (-5x + 7)(x + 1)

Reorder the terms:
6 + 8x + 2x2 = (7 + -5x)(x + 1)

Reorder the terms:
6 + 8x + 2x2 = (7 + -5x)(1 + x)

Multiply (7 + -5x) * (1 + x)
6 + 8x + 2x2 = (7(1 + x) + -5x * (1 + x))
6 + 8x + 2x2 = ((1 * 7 + x * 7) + -5x * (1 + x))
6 + 8x + 2x2 = ((7 + 7x) + -5x * (1 + x))
6 + 8x + 2x2 = (7 + 7x + (1 * -5x + x * -5x))
6 + 8x + 2x2 = (7 + 7x + (-5x + -5x2))

Combine like terms: 7x + -5x = 2x
6 + 8x + 2x2 = (7 + 2x + -5x2)

Solving
6 + 8x + 2x2 = 7 + 2x + -5x2

Solving for variable 'x'.

Reorder the terms:
6 + -7 + 8x + -2x + 2x2 + 5x2 = 7 + 2x + -5x2 + -7 + -2x + 5x2

Combine like terms: 6 + -7 = -1
-1 + 8x + -2x + 2x2 + 5x2 = 7 + 2x + -5x2 + -7 + -2x + 5x2

Combine like terms: 8x + -2x = 6x
-1 + 6x + 2x2 + 5x2 = 7 + 2x + -5x2 + -7 + -2x + 5x2

Combine like terms: 2x2 + 5x2 = 7x2
-1 + 6x + 7x2 = 7 + 2x + -5x2 + -7 + -2x + 5x2

Reorder the terms:
-1 + 6x + 7x2 = 7 + -7 + 2x + -2x + -5x2 + 5x2

Combine like terms: 7 + -7 = 0
-1 + 6x + 7x2 = 0 + 2x + -2x + -5x2 + 5x2
-1 + 6x + 7x2 = 2x + -2x + -5x2 + 5x2

Combine like terms: 2x + -2x = 0
-1 + 6x + 7x2 = 0 + -5x2 + 5x2
-1 + 6x + 7x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-1 + 6x + 7x2 = 0

Factor a trinomial.
(-1 + -1x)(1 + -7x) = 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 '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 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 + -7x = 0 + -1

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

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

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429
Solution
x = {-1, 0.1428571429}

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