(x+5)*(x+9)=x(x+6)+105

Solution for (x+5)*(x+9)=x(x+6)+105 equation:

Simplifying
(x + 5)(x + 9) = x(x + 6) + 105

Reorder the terms:
(5 + x)(x + 9) = x(x + 6) + 105

Reorder the terms:
(5 + x)(9 + x) = x(x + 6) + 105

Multiply (5 + x) * (9 + x)
(5(9 + x) + x(9 + x)) = x(x + 6) + 105
((9 * 5 + x * 5) + x(9 + x)) = x(x + 6) + 105
((45 + 5x) + x(9 + x)) = x(x + 6) + 105
(45 + 5x + (9 * x + x * x)) = x(x + 6) + 105
(45 + 5x + (9x + x2)) = x(x + 6) + 105

Combine like terms: 5x + 9x = 14x
(45 + 14x + x2) = x(x + 6) + 105

Reorder the terms:
45 + 14x + x2 = x(6 + x) + 105
45 + 14x + x2 = (6 * x + x * x) + 105
45 + 14x + x2 = (6x + x2) + 105

Reorder the terms:
45 + 14x + x2 = 105 + 6x + x2

Add '-1x2' to each side of the equation.
45 + 14x + x2 + -1x2 = 105 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
45 + 14x + 0 = 105 + 6x + x2 + -1x2
45 + 14x = 105 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
45 + 14x = 105 + 6x + 0
45 + 14x = 105 + 6x

Solving
45 + 14x = 105 + 6x

Solving for variable 'x'.

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

Add '-6x' to each side of the equation.
45 + 14x + -6x = 105 + 6x + -6x

Combine like terms: 14x + -6x = 8x
45 + 8x = 105 + 6x + -6x

Combine like terms: 6x + -6x = 0
45 + 8x = 105 + 0
45 + 8x = 105

Add '-45' to each side of the equation.
45 + -45 + 8x = 105 + -45

Combine like terms: 45 + -45 = 0
0 + 8x = 105 + -45
8x = 105 + -45

Combine like terms: 105 + -45 = 60
8x = 60

Divide each side by '8'.
x = 7.5

Simplifying
x = 7.5