(x+4)(x+4)-(x+3)(x-3)=1

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Solution for (x+4)(x+4)-(x+3)(x-3)=1 equation: 


Simplifying
(x + 4)(x + 4) + -1(x + 3)(x + -3) = 1

Reorder the terms:
(4 + x)(x + 4) + -1(x + 3)(x + -3) = 1

Reorder the terms:
(4 + x)(4 + x) + -1(x + 3)(x + -3) = 1

Multiply (4 + x) * (4 + x)
(4(4 + x) + x(4 + x)) + -1(x + 3)(x + -3) = 1
((4 * 4 + x * 4) + x(4 + x)) + -1(x + 3)(x + -3) = 1
((16 + 4x) + x(4 + x)) + -1(x + 3)(x + -3) = 1
(16 + 4x + (4 * x + x * x)) + -1(x + 3)(x + -3) = 1
(16 + 4x + (4x + x2)) + -1(x + 3)(x + -3) = 1

Combine like terms: 4x + 4x = 8x
(16 + 8x + x2) + -1(x + 3)(x + -3) = 1

Reorder the terms:
16 + 8x + x2 + -1(3 + x)(x + -3) = 1

Reorder the terms:
16 + 8x + x2 + -1(3 + x)(-3 + x) = 1

Multiply (3 + x) * (-3 + x)
16 + 8x + x2 + -1(3(-3 + x) + x(-3 + x)) = 1
16 + 8x + x2 + -1((-3 * 3 + x * 3) + x(-3 + x)) = 1
16 + 8x + x2 + -1((-9 + 3x) + x(-3 + x)) = 1
16 + 8x + x2 + -1(-9 + 3x + (-3 * x + x * x)) = 1
16 + 8x + x2 + -1(-9 + 3x + (-3x + x2)) = 1

Combine like terms: 3x + -3x = 0
16 + 8x + x2 + -1(-9 + 0 + x2) = 1
16 + 8x + x2 + -1(-9 + x2) = 1
16 + 8x + x2 + (-9 * -1 + x2 * -1) = 1
16 + 8x + x2 + (9 + -1x2) = 1

Reorder the terms:
16 + 9 + 8x + x2 + -1x2 = 1

Combine like terms: 16 + 9 = 25
25 + 8x + x2 + -1x2 = 1

Combine like terms: x2 + -1x2 = 0
25 + 8x + 0 = 1
25 + 8x = 1

Solving
25 + 8x = 1

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + 8x = 1 + -25

Combine like terms: 25 + -25 = 0
0 + 8x = 1 + -25
8x = 1 + -25

Combine like terms: 1 + -25 = -24
8x = -24

Divide each side by '8'.
x = -3

Simplifying
x = -3

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