(2x-7)(x-2)=5

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Solution for (2x-7)(x-2)=5 equation: 


Simplifying
(2x + -7)(x + -2) = 5

Reorder the terms:
(-7 + 2x)(x + -2) = 5

Reorder the terms:
(-7 + 2x)(-2 + x) = 5

Multiply (-7 + 2x) * (-2 + x)
(-7(-2 + x) + 2x * (-2 + x)) = 5
((-2 * -7 + x * -7) + 2x * (-2 + x)) = 5
((14 + -7x) + 2x * (-2 + x)) = 5
(14 + -7x + (-2 * 2x + x * 2x)) = 5
(14 + -7x + (-4x + 2x2)) = 5

Combine like terms: -7x + -4x = -11x
(14 + -11x + 2x2) = 5

Solving
14 + -11x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
14 + -5 + -11x + 2x2 = 5 + -5

Combine like terms: 14 + -5 = 9
9 + -11x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
9 + -11x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(9 + -2x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {1, 4.5}

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