(5+x)(7-x)=0

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Solution for (5+x)(7-x)=0 equation: 


Simplifying
(5 + x)(7 + -1x) = 0

Multiply (5 + x) * (7 + -1x)
(5(7 + -1x) + x(7 + -1x)) = 0
((7 * 5 + -1x * 5) + x(7 + -1x)) = 0
((35 + -5x) + x(7 + -1x)) = 0
(35 + -5x + (7 * x + -1x * x)) = 0
(35 + -5x + (7x + -1x2)) = 0

Combine like terms: -5x + 7x = 2x
(35 + 2x + -1x2) = 0

Solving
35 + 2x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -1x)(5 + 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {7, -5}

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