(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 = 6x
16 + 8x + x2 + -1(9 + 6x + x2) = 1
16 + 8x + x2 + (9 * -1 + 6x * -1 + x2 * -1) = 1
16 + 8x + x2 + (-9 + -6x + -1x2) = 1

Reorder the terms:
16 + -9 + 8x + -6x + x2 + -1x2 = 1

Combine like terms: 16 + -9 = 7
7 + 8x + -6x + x2 + -1x2 = 1

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

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

Solving
7 + 2x = 1

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 1 + -7

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

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

Divide each side by '2'.
x = -3

Simplifying
x = -3

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