(x+2)(x+3)=x*x-10

Solution for (x+2)(x+3)=x*x-10 equation:

Simplifying
(x + 2)(x + 3) = x * x + -10

Reorder the terms:
(2 + x)(x + 3) = x * x + -10

Reorder the terms:
(2 + x)(3 + x) = x * x + -10

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = x * x + -10
((3 * 2 + x * 2) + x(3 + x)) = x * x + -10
((6 + 2x) + x(3 + x)) = x * x + -10
(6 + 2x + (3 * x + x * x)) = x * x + -10
(6 + 2x + (3x + x2)) = x * x + -10

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = x * x + -10

Multiply x * x
6 + 5x + x2 = x2 + -10

Reorder the terms:
6 + 5x + x2 = -10 + x2

Add '-1x2' to each side of the equation.
6 + 5x + x2 + -1x2 = -10 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 5x + 0 = -10 + x2 + -1x2
6 + 5x = -10 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 5x = -10 + 0
6 + 5x = -10

Solving
6 + 5x = -10

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + 5x = -10 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = -10 + -6
5x = -10 + -6

Combine like terms: -10 + -6 = -16
5x = -16

Divide each side by '5'.
x = -3.2

Simplifying
x = -3.2