126=(7+x)(12+x)

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Solution for 126=(7+x)(12+x) equation:


Simplifying
126 = (7 + x)(12 + x)

Multiply (7 + x) * (12 + x)
126 = (7(12 + x) + x(12 + x))
126 = ((12 * 7 + x * 7) + x(12 + x))
126 = ((84 + 7x) + x(12 + x))
126 = (84 + 7x + (12 * x + x * x))
126 = (84 + 7x + (12x + x2))

Combine like terms: 7x + 12x = 19x
126 = (84 + 19x + x2)

Solving
126 = 84 + 19x + x2

Solving for variable 'x'.

Combine like terms: 126 + -84 = 42
42 + -19x + -1x2 = 84 + 19x + x2 + -84 + -19x + -1x2

Reorder the terms:
42 + -19x + -1x2 = 84 + -84 + 19x + -19x + x2 + -1x2

Combine like terms: 84 + -84 = 0
42 + -19x + -1x2 = 0 + 19x + -19x + x2 + -1x2
42 + -19x + -1x2 = 19x + -19x + x2 + -1x2

Combine like terms: 19x + -19x = 0
42 + -19x + -1x2 = 0 + x2 + -1x2
42 + -19x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + -19x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(21 + 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 '(21 + x)' equal to zero and attempt to solve: Simplifying 21 + x = 0 Solving 21 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + x = 0 + -21 x = 0 + -21 Combine like terms: 0 + -21 = -21 x = -21 Simplifying x = -21

Solution

x = {2, -21}

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