266=(7+x)(12+x)

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Solution for 266=(7+x)(12+x) equation: 


Simplifying
266 = (7 + x)(12 + x)

Multiply (7 + x) * (12 + x)
266 = (7(12 + x) + x(12 + x))
266 = ((12 * 7 + x * 7) + x(12 + x))
266 = ((84 + 7x) + x(12 + x))
266 = (84 + 7x + (12 * x + x * x))
266 = (84 + 7x + (12x + x2))

Combine like terms: 7x + 12x = 19x
266 = (84 + 19x + x2)

Solving
266 = 84 + 19x + x2

Solving for variable 'x'.

Combine like terms: 266 + -84 = 182
182 + -19x + -1x2 = 84 + 19x + x2 + -84 + -19x + -1x2

Reorder the terms:
182 + -19x + -1x2 = 84 + -84 + 19x + -19x + x2 + -1x2

Combine like terms: 84 + -84 = 0
182 + -19x + -1x2 = 0 + 19x + -19x + x2 + -1x2
182 + -19x + -1x2 = 19x + -19x + x2 + -1x2

Combine like terms: 19x + -19x = 0
182 + -19x + -1x2 = 0 + x2 + -1x2
182 + -19x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
182 + -19x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(26 + x) = 0


Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

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

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

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(26 + x)' equal to zero and attempt to solve:

Simplifying
26 + x = 0

Solving
26 + x = 0

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

Add '-26' to each side of the equation.
26 + -26 + x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + x = 0 + -26
x = 0 + -26

Combine like terms: 0 + -26 = -26
x = -26

Simplifying
x = -26
Solution
x = {7, -26}

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