140+10x=20+12x+x^2

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Solution for 140+10x=20+12x+x^2 equation: 


Simplifying
140 + 10x = 20 + 12x + x2

Solving
140 + 10x = 20 + 12x + x2

Solving for variable 'x'.

Reorder the terms:
140 + -20 + 10x + -12x + -1x2 = 20 + 12x + x2 + -20 + -12x + -1x2

Combine like terms: 140 + -20 = 120
120 + 10x + -12x + -1x2 = 20 + 12x + x2 + -20 + -12x + -1x2

Combine like terms: 10x + -12x = -2x
120 + -2x + -1x2 = 20 + 12x + x2 + -20 + -12x + -1x2

Reorder the terms:
120 + -2x + -1x2 = 20 + -20 + 12x + -12x + x2 + -1x2

Combine like terms: 20 + -20 = 0
120 + -2x + -1x2 = 0 + 12x + -12x + x2 + -1x2
120 + -2x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
120 + -2x + -1x2 = 0 + x2 + -1x2
120 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
120 + -2x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(12 + x) = 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 '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {10, -12}

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