(x+4)(x-4)-(x-3)(x-3)=x(6-x)

Solution for (x+4)(x-4)-(x-3)(x-3)=x(6-x) equation:

Simplifying
(x + 4)(x + -4) + -1(x + -3)(x + -3) = x(6 + -1x)

Reorder the terms:
(4 + x)(x + -4) + -1(x + -3)(x + -3) = x(6 + -1x)

Reorder the terms:
(4 + x)(-4 + x) + -1(x + -3)(x + -3) = x(6 + -1x)

Multiply (4 + x) * (-4 + x)
(4(-4 + x) + x(-4 + x)) + -1(x + -3)(x + -3) = x(6 + -1x)
((-4 * 4 + x * 4) + x(-4 + x)) + -1(x + -3)(x + -3) = x(6 + -1x)
((-16 + 4x) + x(-4 + x)) + -1(x + -3)(x + -3) = x(6 + -1x)
(-16 + 4x + (-4 * x + x * x)) + -1(x + -3)(x + -3) = x(6 + -1x)
(-16 + 4x + (-4x + x2)) + -1(x + -3)(x + -3) = x(6 + -1x)

Combine like terms: 4x + -4x = 0
(-16 + 0 + x2) + -1(x + -3)(x + -3) = x(6 + -1x)
(-16 + x2) + -1(x + -3)(x + -3) = x(6 + -1x)

Reorder the terms:
-16 + x2 + -1(-3 + x)(x + -3) = x(6 + -1x)

Reorder the terms:
-16 + x2 + -1(-3 + x)(-3 + x) = x(6 + -1x)

Multiply (-3 + x) * (-3 + x)
-16 + x2 + -1(-3(-3 + x) + x(-3 + x)) = x(6 + -1x)
-16 + x2 + -1((-3 * -3 + x * -3) + x(-3 + x)) = x(6 + -1x)
-16 + x2 + -1((9 + -3x) + x(-3 + x)) = x(6 + -1x)
-16 + x2 + -1(9 + -3x + (-3 * x + x * x)) = x(6 + -1x)
-16 + x2 + -1(9 + -3x + (-3x + x2)) = x(6 + -1x)

Combine like terms: -3x + -3x = -6x
-16 + x2 + -1(9 + -6x + x2) = x(6 + -1x)
-16 + x2 + (9 * -1 + -6x * -1 + x2 * -1) = x(6 + -1x)
-16 + x2 + (-9 + 6x + -1x2) = x(6 + -1x)

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

Combine like terms: -16 + -9 = -25
-25 + 6x + x2 + -1x2 = x(6 + -1x)

Combine like terms: x2 + -1x2 = 0
-25 + 6x + 0 = x(6 + -1x)
-25 + 6x = x(6 + -1x)
-25 + 6x = (6 * x + -1x * x)
-25 + 6x = (6x + -1x2)

Add '-6x' to each side of the equation.
-25 + 6x + -6x = 6x + -6x + -1x2

Combine like terms: 6x + -6x = 0
-25 + 0 = 6x + -6x + -1x2
-25 = 6x + -6x + -1x2

Combine like terms: 6x + -6x = 0
-25 = 0 + -1x2
-25 = -1x2

Solving
-25 = -1x2

Solving for variable 'x'.

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

Add 'x2' to each side of the equation.
-25 + x2 = -1x2 + x2

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

Add '25' to each side of the equation.
-25 + 25 + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + x2 = 0 + 25
x2 = 0 + 25

Combine like terms: 0 + 25 = 25
x2 = 25

Simplifying
x2 = 25

Take the square root of each side:
x = {-5, 5}