x^2-4x+45=10x+5

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Solution for x^2-4x+45=10x+5 equation: 


Simplifying
x2 + -4x + 45 = 10x + 5

Reorder the terms:
45 + -4x + x2 = 10x + 5

Reorder the terms:
45 + -4x + x2 = 5 + 10x

Solving
45 + -4x + x2 = 5 + 10x

Solving for variable 'x'.

Reorder the terms:
45 + -5 + -4x + -10x + x2 = 5 + 10x + -5 + -10x

Combine like terms: 45 + -5 = 40
40 + -4x + -10x + x2 = 5 + 10x + -5 + -10x

Combine like terms: -4x + -10x = -14x
40 + -14x + x2 = 5 + 10x + -5 + -10x

Reorder the terms:
40 + -14x + x2 = 5 + -5 + 10x + -10x

Combine like terms: 5 + -5 = 0
40 + -14x + x2 = 0 + 10x + -10x
40 + -14x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
40 + -14x + x2 = 0

Factor a trinomial.
(4 + -1x)(10 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {4, 10}

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