(x-7)(x-4)=208

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Solution for (x-7)(x-4)=208 equation: 


Simplifying
(x + -7)(x + -4) = 208

Reorder the terms:
(-7 + x)(x + -4) = 208

Reorder the terms:
(-7 + x)(-4 + x) = 208

Multiply (-7 + x) * (-4 + x)
(-7(-4 + x) + x(-4 + x)) = 208
((-4 * -7 + x * -7) + x(-4 + x)) = 208
((28 + -7x) + x(-4 + x)) = 208
(28 + -7x + (-4 * x + x * x)) = 208
(28 + -7x + (-4x + x2)) = 208

Combine like terms: -7x + -4x = -11x
(28 + -11x + x2) = 208

Solving
28 + -11x + x2 = 208

Solving for variable 'x'.

Reorder the terms:
28 + -208 + -11x + x2 = 208 + -208

Combine like terms: 28 + -208 = -180
-180 + -11x + x2 = 208 + -208

Combine like terms: 208 + -208 = 0
-180 + -11x + x2 = 0

Factor a trinomial.
(-9 + -1x)(20 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-9, 20}

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