(2x-8)*(x-7)=0

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Solution for (2x-8)*(x-7)=0 equation: 


Simplifying
(2x + -8)(x + -7) = 0

Reorder the terms:
(-8 + 2x)(x + -7) = 0

Reorder the terms:
(-8 + 2x)(-7 + x) = 0

Multiply (-8 + 2x) * (-7 + x)
(-8(-7 + x) + 2x * (-7 + x)) = 0
((-7 * -8 + x * -8) + 2x * (-7 + x)) = 0
((56 + -8x) + 2x * (-7 + x)) = 0
(56 + -8x + (-7 * 2x + x * 2x)) = 0
(56 + -8x + (-14x + 2x2)) = 0

Combine like terms: -8x + -14x = -22x
(56 + -22x + 2x2) = 0

Solving
56 + -22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -11x + x2) = 0

Factor a trinomial.
2((4 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

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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