x^2-5x-14=-10x+22

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Solution for x^2-5x-14=-10x+22 equation:


Simplifying
x2 + -5x + -14 = -10x + 22

Reorder the terms:
-14 + -5x + x2 = -10x + 22

Reorder the terms:
-14 + -5x + x2 = 22 + -10x

Solving
-14 + -5x + x2 = 22 + -10x

Solving for variable 'x'.

Reorder the terms:
-14 + -22 + -5x + 10x + x2 = 22 + -10x + -22 + 10x

Combine like terms: -14 + -22 = -36
-36 + -5x + 10x + x2 = 22 + -10x + -22 + 10x

Combine like terms: -5x + 10x = 5x
-36 + 5x + x2 = 22 + -10x + -22 + 10x

Reorder the terms:
-36 + 5x + x2 = 22 + -22 + -10x + 10x

Combine like terms: 22 + -22 = 0
-36 + 5x + x2 = 0 + -10x + 10x
-36 + 5x + x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
-36 + 5x + x2 = 0

Factor a trinomial.
(-9 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 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 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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 = {-9, 4}

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