4x-10=5x-x^2+20

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Solution for 4x-10=5x-x^2+20 equation: 


Simplifying
4x + -10 = 5x + -1x2 + 20

Reorder the terms:
-10 + 4x = 5x + -1x2 + 20

Reorder the terms:
-10 + 4x = 20 + 5x + -1x2

Solving
-10 + 4x = 20 + 5x + -1x2

Solving for variable 'x'.

Reorder the terms:
-10 + -20 + 4x + -5x + x2 = 20 + 5x + -1x2 + -20 + -5x + x2

Combine like terms: -10 + -20 = -30
-30 + 4x + -5x + x2 = 20 + 5x + -1x2 + -20 + -5x + x2

Combine like terms: 4x + -5x = -1x
-30 + -1x + x2 = 20 + 5x + -1x2 + -20 + -5x + x2

Reorder the terms:
-30 + -1x + x2 = 20 + -20 + 5x + -5x + -1x2 + x2

Combine like terms: 20 + -20 = 0
-30 + -1x + x2 = 0 + 5x + -5x + -1x2 + x2
-30 + -1x + x2 = 5x + -5x + -1x2 + x2

Combine like terms: 5x + -5x = 0
-30 + -1x + x2 = 0 + -1x2 + x2
-30 + -1x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-30 + -1x + x2 = 0

Factor a trinomial.
(-5 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-5, 6}

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