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

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


Simplifying
(x + -7)(x + -4) = 4

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

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

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

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

Solving
28 + -11x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
28 + -4 + -11x + x2 = 4 + -4

Combine like terms: 28 + -4 = 24
24 + -11x + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
24 + -11x + x2 = 0

Factor a trinomial.
(3 + -1x)(8 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {3, 8}

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