(2x+1)(x-1)=(x+7)(x+8)

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Solution for (2x+1)(x-1)=(x+7)(x+8) equation: 


Simplifying
(2x + 1)(x + -1) = (x + 7)(x + 8)

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

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

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

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

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

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

Multiply (7 + x) * (8 + x)
-1 + -1x + 2x2 = (7(8 + x) + x(8 + x))
-1 + -1x + 2x2 = ((8 * 7 + x * 7) + x(8 + x))
-1 + -1x + 2x2 = ((56 + 7x) + x(8 + x))
-1 + -1x + 2x2 = (56 + 7x + (8 * x + x * x))
-1 + -1x + 2x2 = (56 + 7x + (8x + x2))

Combine like terms: 7x + 8x = 15x
-1 + -1x + 2x2 = (56 + 15x + x2)

Solving
-1 + -1x + 2x2 = 56 + 15x + x2

Solving for variable 'x'.

Reorder the terms:
-1 + -56 + -1x + -15x + 2x2 + -1x2 = 56 + 15x + x2 + -56 + -15x + -1x2

Combine like terms: -1 + -56 = -57
-57 + -1x + -15x + 2x2 + -1x2 = 56 + 15x + x2 + -56 + -15x + -1x2

Combine like terms: -1x + -15x = -16x
-57 + -16x + 2x2 + -1x2 = 56 + 15x + x2 + -56 + -15x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-57 + -16x + 1x2 = 56 + 15x + x2 + -56 + -15x + -1x2

Reorder the terms:
-57 + -16x + 1x2 = 56 + -56 + 15x + -15x + x2 + -1x2

Combine like terms: 56 + -56 = 0
-57 + -16x + 1x2 = 0 + 15x + -15x + x2 + -1x2
-57 + -16x + 1x2 = 15x + -15x + x2 + -1x2

Combine like terms: 15x + -15x = 0
-57 + -16x + 1x2 = 0 + x2 + -1x2
-57 + -16x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-57 + -16x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(19 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Solution
x = {-3, 19}

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