(2x-7)*(x-5)=14

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Solution for (2x-7)*(x-5)=14 equation: 


Simplifying
(2x + -7)(x + -5) = 14

Reorder the terms:
(-7 + 2x)(x + -5) = 14

Reorder the terms:
(-7 + 2x)(-5 + x) = 14

Multiply (-7 + 2x) * (-5 + x)
(-7(-5 + x) + 2x * (-5 + x)) = 14
((-5 * -7 + x * -7) + 2x * (-5 + x)) = 14
((35 + -7x) + 2x * (-5 + x)) = 14
(35 + -7x + (-5 * 2x + x * 2x)) = 14
(35 + -7x + (-10x + 2x2)) = 14

Combine like terms: -7x + -10x = -17x
(35 + -17x + 2x2) = 14

Solving
35 + -17x + 2x2 = 14

Solving for variable 'x'.

Reorder the terms:
35 + -14 + -17x + 2x2 = 14 + -14

Combine like terms: 35 + -14 = 21
21 + -17x + 2x2 = 14 + -14

Combine like terms: 14 + -14 = 0
21 + -17x + 2x2 = 0

Factor a trinomial.
(3 + -2x)(7 + -1x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

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 = {1.5, 7}

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