10x+140=(x+10)(x+2)

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Solution for 10x+140=(x+10)(x+2) equation: 


Simplifying
10x + 140 = (x + 10)(x + 2)

Reorder the terms:
140 + 10x = (x + 10)(x + 2)

Reorder the terms:
140 + 10x = (10 + x)(x + 2)

Reorder the terms:
140 + 10x = (10 + x)(2 + x)

Multiply (10 + x) * (2 + x)
140 + 10x = (10(2 + x) + x(2 + x))
140 + 10x = ((2 * 10 + x * 10) + x(2 + x))
140 + 10x = ((20 + 10x) + x(2 + x))
140 + 10x = (20 + 10x + (2 * x + x * x))
140 + 10x = (20 + 10x + (2x + x2))

Combine like terms: 10x + 2x = 12x
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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