3x+43=x^2+10x+25

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Solution for 3x+43=x^2+10x+25 equation: 


Simplifying
3x + 43 = x2 + 10x + 25

Reorder the terms:
43 + 3x = x2 + 10x + 25

Reorder the terms:
43 + 3x = 25 + 10x + x2

Solving
43 + 3x = 25 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
43 + -25 + 3x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 43 + -25 = 18
18 + 3x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 3x + -10x = -7x
18 + -7x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Reorder the terms:
18 + -7x + -1x2 = 25 + -25 + 10x + -10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
18 + -7x + -1x2 = 0 + 10x + -10x + x2 + -1x2
18 + -7x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
18 + -7x + -1x2 = 0 + x2 + -1x2
18 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
18 + -7x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(9 + x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {2, -9}

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