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

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


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

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

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

Multiply (-7 + x) * (7 + x)
(-7(7 + x) + x(7 + x)) = (x + 8)(x + 8) + -1
((7 * -7 + x * -7) + x(7 + x)) = (x + 8)(x + 8) + -1
((-49 + -7x) + x(7 + x)) = (x + 8)(x + 8) + -1
(-49 + -7x + (7 * x + x * x)) = (x + 8)(x + 8) + -1
(-49 + -7x + (7x + x2)) = (x + 8)(x + 8) + -1

Combine like terms: -7x + 7x = 0
(-49 + 0 + x2) = (x + 8)(x + 8) + -1
(-49 + x2) = (x + 8)(x + 8) + -1

Reorder the terms:
-49 + x2 = (8 + x)(x + 8) + -1

Reorder the terms:
-49 + x2 = (8 + x)(8 + x) + -1

Multiply (8 + x) * (8 + x)
-49 + x2 = (8(8 + x) + x(8 + x)) + -1
-49 + x2 = ((8 * 8 + x * 8) + x(8 + x)) + -1
-49 + x2 = ((64 + 8x) + x(8 + x)) + -1
-49 + x2 = (64 + 8x + (8 * x + x * x)) + -1
-49 + x2 = (64 + 8x + (8x + x2)) + -1

Combine like terms: 8x + 8x = 16x
-49 + x2 = (64 + 16x + x2) + -1

Reorder the terms:
-49 + x2 = 64 + -1 + 16x + x2

Combine like terms: 64 + -1 = 63
-49 + x2 = 63 + 16x + x2

Add '-1x2' to each side of the equation.
-49 + x2 + -1x2 = 63 + 16x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-49 + 0 = 63 + 16x + x2 + -1x2
-49 = 63 + 16x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-49 = 63 + 16x + 0
-49 = 63 + 16x

Solving
-49 = 63 + 16x

Solving for variable 'x'.

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

Add '-16x' to each side of the equation.
-49 + -16x = 63 + 16x + -16x

Combine like terms: 16x + -16x = 0
-49 + -16x = 63 + 0
-49 + -16x = 63

Add '49' to each side of the equation.
-49 + 49 + -16x = 63 + 49

Combine like terms: -49 + 49 = 0
0 + -16x = 63 + 49
-16x = 63 + 49

Combine like terms: 63 + 49 = 112
-16x = 112

Divide each side by '-16'.
x = -7

Simplifying
x = -7

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