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

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


Simplifying
x2 + -2x + -10 = -4x + 5

Reorder the terms:
-10 + -2x + x2 = -4x + 5

Reorder the terms:
-10 + -2x + x2 = 5 + -4x

Solving
-10 + -2x + x2 = 5 + -4x

Solving for variable 'x'.

Reorder the terms:
-10 + -5 + -2x + 4x + x2 = 5 + -4x + -5 + 4x

Combine like terms: -10 + -5 = -15
-15 + -2x + 4x + x2 = 5 + -4x + -5 + 4x

Combine like terms: -2x + 4x = 2x
-15 + 2x + x2 = 5 + -4x + -5 + 4x

Reorder the terms:
-15 + 2x + x2 = 5 + -5 + -4x + 4x

Combine like terms: 5 + -5 = 0
-15 + 2x + x2 = 0 + -4x + 4x
-15 + 2x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-15 + 2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-5, 3}

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