x^2-2x-10=3x-14

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Solution for x^2-2x-10=3x-14 equation: 


Simplifying
x2 + -2x + -10 = 3x + -14

Reorder the terms:
-10 + -2x + x2 = 3x + -14

Reorder the terms:
-10 + -2x + x2 = -14 + 3x

Solving
-10 + -2x + x2 = -14 + 3x

Solving for variable 'x'.

Reorder the terms:
-10 + 14 + -2x + -3x + x2 = -14 + 3x + 14 + -3x

Combine like terms: -10 + 14 = 4
4 + -2x + -3x + x2 = -14 + 3x + 14 + -3x

Combine like terms: -2x + -3x = -5x
4 + -5x + x2 = -14 + 3x + 14 + -3x

Reorder the terms:
4 + -5x + x2 = -14 + 14 + 3x + -3x

Combine like terms: -14 + 14 = 0
4 + -5x + x2 = 0 + 3x + -3x
4 + -5x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
4 + -5x + x2 = 0

Factor a trinomial.
(1 + -1x)(4 + -1x) = 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 '(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
Solution
x = {1, 4}

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