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

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

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

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

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

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

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

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

Add '-1x2' to each side of the equation.
-6 + 1x + x2 + -1x2 = 7x + x2 + -1x2

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

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

Solving
-6 + 1x = 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.
-6 + 1x + -7x = 7x + -7x

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

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

Add '6' to each side of the equation.
-6 + 6 + -6x = 0 + 6

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

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

Divide each side by '-6'.
x = -1

Simplifying
x = -1