(2x+1)(x+7)=(x+5)(x-3)

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Solution for (2x+1)(x+7)=(x+5)(x-3) equation: 


Simplifying
(2x + 1)(x + 7) = (x + 5)(x + -3)

Reorder the terms:
(1 + 2x)(x + 7) = (x + 5)(x + -3)

Reorder the terms:
(1 + 2x)(7 + x) = (x + 5)(x + -3)

Multiply (1 + 2x) * (7 + x)
(1(7 + x) + 2x * (7 + x)) = (x + 5)(x + -3)
((7 * 1 + x * 1) + 2x * (7 + x)) = (x + 5)(x + -3)
((7 + 1x) + 2x * (7 + x)) = (x + 5)(x + -3)
(7 + 1x + (7 * 2x + x * 2x)) = (x + 5)(x + -3)
(7 + 1x + (14x + 2x2)) = (x + 5)(x + -3)

Combine like terms: 1x + 14x = 15x
(7 + 15x + 2x2) = (x + 5)(x + -3)

Reorder the terms:
7 + 15x + 2x2 = (5 + x)(x + -3)

Reorder the terms:
7 + 15x + 2x2 = (5 + x)(-3 + x)

Multiply (5 + x) * (-3 + x)
7 + 15x + 2x2 = (5(-3 + x) + x(-3 + x))
7 + 15x + 2x2 = ((-3 * 5 + x * 5) + x(-3 + x))
7 + 15x + 2x2 = ((-15 + 5x) + x(-3 + x))
7 + 15x + 2x2 = (-15 + 5x + (-3 * x + x * x))
7 + 15x + 2x2 = (-15 + 5x + (-3x + x2))

Combine like terms: 5x + -3x = 2x
7 + 15x + 2x2 = (-15 + 2x + x2)

Solving
7 + 15x + 2x2 = -15 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
7 + 15 + 15x + -2x + 2x2 + -1x2 = -15 + 2x + x2 + 15 + -2x + -1x2

Combine like terms: 7 + 15 = 22
22 + 15x + -2x + 2x2 + -1x2 = -15 + 2x + x2 + 15 + -2x + -1x2

Combine like terms: 15x + -2x = 13x
22 + 13x + 2x2 + -1x2 = -15 + 2x + x2 + 15 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
22 + 13x + 1x2 = -15 + 2x + x2 + 15 + -2x + -1x2

Reorder the terms:
22 + 13x + 1x2 = -15 + 15 + 2x + -2x + x2 + -1x2

Combine like terms: -15 + 15 = 0
22 + 13x + 1x2 = 0 + 2x + -2x + x2 + -1x2
22 + 13x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
22 + 13x + 1x2 = 0 + x2 + -1x2
22 + 13x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
22 + 13x + 1x2 = 0

Factor a trinomial.
(11 + x)(2 + x) = 0


Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11

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 = {-11, -2}

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