(6+x)(4+x)=63

Solution for (6+x)(4+x)=63 equation:

Simplifying
(6 + x)(4 + x) = 63

Multiply (6 + x) * (4 + x)
(6(4 + x) + x(4 + x)) = 63
((4 * 6 + x * 6) + x(4 + x)) = 63
((24 + 6x) + x(4 + x)) = 63
(24 + 6x + (4 * x + x * x)) = 63
(24 + 6x + (4x + x2)) = 63

Combine like terms: 6x + 4x = 10x
(24 + 10x + x2) = 63

Solving
24 + 10x + x2 = 63

Solving for variable 'x'.

Reorder the terms:
24 + -63 + 10x + x2 = 63 + -63

Combine like terms: 24 + -63 = -39
-39 + 10x + x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-39 + 10x + x2 = 0

Factor a trinomial.
(-13 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-13, 3}