x^2-4x=14-9x

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Solution for x^2-4x=14-9x equation: 


Simplifying
x2 + -4x = 14 + -9x

Reorder the terms:
-4x + x2 = 14 + -9x

Solving
-4x + x2 = 14 + -9x

Solving for variable 'x'.

Reorder the terms:
-14 + -4x + 9x + x2 = 14 + -9x + -14 + 9x

Combine like terms: -4x + 9x = 5x
-14 + 5x + x2 = 14 + -9x + -14 + 9x

Reorder the terms:
-14 + 5x + x2 = 14 + -14 + -9x + 9x

Combine like terms: 14 + -14 = 0
-14 + 5x + x2 = 0 + -9x + 9x
-14 + 5x + x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-14 + 5x + x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-7, 2}

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