2x(x-5)=x-14

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


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

Reorder the terms:
2x(-5 + x) = x + -14
(-5 * 2x + x * 2x) = x + -14
(-10x + 2x2) = x + -14

Reorder the terms:
-10x + 2x2 = -14 + x

Solving
-10x + 2x2 = -14 + x

Solving for variable 'x'.

Reorder the terms:
14 + -10x + -1x + 2x2 = -14 + x + 14 + -1x

Combine like terms: -10x + -1x = -11x
14 + -11x + 2x2 = -14 + x + 14 + -1x

Reorder the terms:
14 + -11x + 2x2 = -14 + 14 + x + -1x

Combine like terms: -14 + 14 = 0
14 + -11x + 2x2 = 0 + x + -1x
14 + -11x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
14 + -11x + 2x2 = 0

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


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {2, 3.5}

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