x^2+10x-25=3x+5

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Solution for x^2+10x-25=3x+5 equation: 


Simplifying
x2 + 10x + -25 = 3x + 5

Reorder the terms:
-25 + 10x + x2 = 3x + 5

Reorder the terms:
-25 + 10x + x2 = 5 + 3x

Solving
-25 + 10x + x2 = 5 + 3x

Solving for variable 'x'.

Reorder the terms:
-25 + -5 + 10x + -3x + x2 = 5 + 3x + -5 + -3x

Combine like terms: -25 + -5 = -30
-30 + 10x + -3x + x2 = 5 + 3x + -5 + -3x

Combine like terms: 10x + -3x = 7x
-30 + 7x + x2 = 5 + 3x + -5 + -3x

Reorder the terms:
-30 + 7x + x2 = 5 + -5 + 3x + -3x

Combine like terms: 5 + -5 = 0
-30 + 7x + x2 = 0 + 3x + -3x
-30 + 7x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-30 + 7x + x2 = 0

Factor a trinomial.
(-10 + -1x)(3 + -1x) = 0


Subproblem 1
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

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 = {-10, 3}

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