(x+2)(x+3)-x(x+4)=7

Solution for (x+2)(x+3)-x(x+4)=7 equation:

Simplifying
(x + 2)(x + 3) + -1x(x + 4) = 7

Reorder the terms:
(2 + x)(x + 3) + -1x(x + 4) = 7

Reorder the terms:
(2 + x)(3 + x) + -1x(x + 4) = 7

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) + -1x(x + 4) = 7
((3 * 2 + x * 2) + x(3 + x)) + -1x(x + 4) = 7
((6 + 2x) + x(3 + x)) + -1x(x + 4) = 7
(6 + 2x + (3 * x + x * x)) + -1x(x + 4) = 7
(6 + 2x + (3x + x2)) + -1x(x + 4) = 7

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) + -1x(x + 4) = 7

Reorder the terms:
6 + 5x + x2 + -1x(4 + x) = 7
6 + 5x + x2 + (4 * -1x + x * -1x) = 7
6 + 5x + x2 + (-4x + -1x2) = 7

Reorder the terms:
6 + 5x + -4x + x2 + -1x2 = 7

Combine like terms: 5x + -4x = 1x
6 + 1x + x2 + -1x2 = 7

Combine like terms: x2 + -1x2 = 0
6 + 1x + 0 = 7
6 + 1x = 7

Solving
6 + 1x = 7

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 + 1x = 7 + -6

Combine like terms: 6 + -6 = 0
0 + 1x = 7 + -6
1x = 7 + -6

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

Divide each side by '1'.
x = 1

Simplifying
x = 1