x^2-10=3x+30

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Solution for x^2-10=3x+30 equation: 


Simplifying
x2 + -10 = 3x + 30

Reorder the terms:
-10 + x2 = 3x + 30

Reorder the terms:
-10 + x2 = 30 + 3x

Solving
-10 + x2 = 30 + 3x

Solving for variable 'x'.

Reorder the terms:
-10 + -30 + -3x + x2 = 30 + 3x + -30 + -3x

Combine like terms: -10 + -30 = -40
-40 + -3x + x2 = 30 + 3x + -30 + -3x

Reorder the terms:
-40 + -3x + x2 = 30 + -30 + 3x + -3x

Combine like terms: 30 + -30 = 0
-40 + -3x + x2 = 0 + 3x + -3x
-40 + -3x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-40 + -3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-5, 8}

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