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

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


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

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

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

Multiply (-3 + x) * (3 + x)
(-3(3 + x) + x(3 + x)) + -1x(x + -4) = 1
((3 * -3 + x * -3) + x(3 + x)) + -1x(x + -4) = 1
((-9 + -3x) + x(3 + x)) + -1x(x + -4) = 1
(-9 + -3x + (3 * x + x * x)) + -1x(x + -4) = 1
(-9 + -3x + (3x + x2)) + -1x(x + -4) = 1

Combine like terms: -3x + 3x = 0
(-9 + 0 + x2) + -1x(x + -4) = 1
(-9 + x2) + -1x(x + -4) = 1

Reorder the terms:
-9 + x2 + -1x(-4 + x) = 1
-9 + x2 + (-4 * -1x + x * -1x) = 1
-9 + x2 + (4x + -1x2) = 1

Reorder the terms:
-9 + 4x + x2 + -1x2 = 1

Combine like terms: x2 + -1x2 = 0
-9 + 4x + 0 = 1
-9 + 4x = 1

Solving
-9 + 4x = 1

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + 4x = 1 + 9

Combine like terms: -9 + 9 = 0
0 + 4x = 1 + 9
4x = 1 + 9

Combine like terms: 1 + 9 = 10
4x = 10

Divide each side by '4'.
x = 2.5

Simplifying
x = 2.5

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