(10+x)(x+2)=(x+14)10

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Solution for (10+x)(x+2)=(x+14)10 equation: 


Simplifying
(10 + x)(x + 2) = (x + 14) * 10

Reorder the terms:
(10 + x)(2 + x) = (x + 14) * 10

Multiply (10 + x) * (2 + x)
(10(2 + x) + x(2 + x)) = (x + 14) * 10
((2 * 10 + x * 10) + x(2 + x)) = (x + 14) * 10
((20 + 10x) + x(2 + x)) = (x + 14) * 10
(20 + 10x + (2 * x + x * x)) = (x + 14) * 10
(20 + 10x + (2x + x2)) = (x + 14) * 10

Combine like terms: 10x + 2x = 12x
(20 + 12x + x2) = (x + 14) * 10

Reorder the terms:
20 + 12x + x2 = (14 + x) * 10

Reorder the terms for easier multiplication:
20 + 12x + x2 = 10(14 + x)
20 + 12x + x2 = (14 * 10 + x * 10)
20 + 12x + x2 = (140 + 10x)

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

Solving for variable 'x'.

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

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

Combine like terms: 12x + -10x = 2x
-120 + 2x + x2 = 140 + 10x + -140 + -10x

Reorder the terms:
-120 + 2x + x2 = 140 + -140 + 10x + -10x

Combine like terms: 140 + -140 = 0
-120 + 2x + x2 = 0 + 10x + -10x
-120 + 2x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-120 + 2x + x2 = 0

Factor a trinomial.
(-12 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 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 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

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 = {-12, 10}

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