(x-4)x-(x-4)7=0

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Solution for (x-4)x-(x-4)7=0 equation: 


Simplifying
(x + -4) * x + -1(x + -4) * 7 = 0

Reorder the terms:
(-4 + x) * x + -1(x + -4) * 7 = 0

Reorder the terms for easier multiplication:
x(-4 + x) + -1(x + -4) * 7 = 0
(-4 * x + x * x) + -1(x + -4) * 7 = 0
(-4x + x2) + -1(x + -4) * 7 = 0

Reorder the terms:
-4x + x2 + -1(-4 + x) * 7 = 0

Reorder the terms for easier multiplication:
-4x + x2 + -1 * 7(-4 + x) = 0

Multiply -1 * 7
-4x + x2 + -7(-4 + x) = 0
-4x + x2 + (-4 * -7 + x * -7) = 0
-4x + x2 + (28 + -7x) = 0

Reorder the terms:
28 + -4x + -7x + x2 = 0

Combine like terms: -4x + -7x = -11x
28 + -11x + x2 = 0

Solving
28 + -11x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

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

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

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {4, 7}

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