(x+10)(x+4)=x^2+wx+40

Solution for (x+10)(x+4)=x^2+wx+40 equation:

Simplifying
(x + 10)(x + 4) = x2 + wx + 40

Reorder the terms:
(10 + x)(x + 4) = x2 + wx + 40

Reorder the terms:
(10 + x)(4 + x) = x2 + wx + 40

Multiply (10 + x) * (4 + x)
(10(4 + x) + x(4 + x)) = x2 + wx + 40
((4 * 10 + x * 10) + x(4 + x)) = x2 + wx + 40
((40 + 10x) + x(4 + x)) = x2 + wx + 40
(40 + 10x + (4 * x + x * x)) = x2 + wx + 40
(40 + 10x + (4x + x2)) = x2 + wx + 40

Combine like terms: 10x + 4x = 14x
(40 + 14x + x2) = x2 + wx + 40

Reorder the terms:
40 + 14x + x2 = 40 + wx + x2

Add '-40' to each side of the equation.
40 + 14x + -40 + x2 = 40 + wx + -40 + x2

Reorder the terms:
40 + -40 + 14x + x2 = 40 + wx + -40 + x2

Combine like terms: 40 + -40 = 0
0 + 14x + x2 = 40 + wx + -40 + x2
14x + x2 = 40 + wx + -40 + x2

Reorder the terms:
14x + x2 = 40 + -40 + wx + x2

Combine like terms: 40 + -40 = 0
14x + x2 = 0 + wx + x2
14x + x2 = wx + x2

Add '-1x2' to each side of the equation.
14x + x2 + -1x2 = wx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14x + 0 = wx + x2 + -1x2
14x = wx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14x = wx + 0
14x = wx

Solving
14x = wx

Solving for variable 'x'.

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

Add '-1wx' to each side of the equation.
-1wx + 14x = wx + -1wx

Combine like terms: wx + -1wx = 0
-1wx + 14x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1w + 14) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1w + 14)' equal to zero and attempt to solve:

Simplifying
-1w + 14 = 0

Reorder the terms:
14 + -1w = 0

Solving
14 + -1w = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1w = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1w = 0 + -14
-1w = 0 + -14

Combine like terms: 0 + -14 = -14
-1w = -14

Add 'w' to each side of the equation.
-1w + w = -14 + w

Combine like terms: -1w + w = 0
0 = -14 + w

Simplifying
0 = -14 + w

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}