(x-6)(x+7)=x^2

Solution for (x-6)(x+7)=x^2 equation:

Simplifying
(x + -6)(x + 7) = x2

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

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

Multiply (-6 + x) * (7 + x)
(-6(7 + x) + x(7 + x)) = x2
((7 * -6 + x * -6) + x(7 + x)) = x2
((-42 + -6x) + x(7 + x)) = x2
(-42 + -6x + (7 * x + x * x)) = x2
(-42 + -6x + (7x + x2)) = x2

Combine like terms: -6x + 7x = 1x
(-42 + 1x + x2) = x2

Add '-1x2' to each side of the equation.
-42 + 1x + x2 + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-42 + 1x + 0 = x2 + -1x2
-42 + 1x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-42 + 1x = 0

Solving
-42 + 1x = 0

Solving for variable 'x'.

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

Add '42' to each side of the equation.
-42 + 42 + 1x = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 1x = 0 + 42
1x = 0 + 42

Combine like terms: 0 + 42 = 42
1x = 42

Divide each side by '1'.
x = 42

Simplifying
x = 42