(x-5)(x+7)=28

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Solution for (x-5)(x+7)=28 equation: 


Simplifying
(x + -5)(x + 7) = 28

Reorder the terms:
(-5 + x)(x + 7) = 28

Reorder the terms:
(-5 + x)(7 + x) = 28

Multiply (-5 + x) * (7 + x)
(-5(7 + x) + x(7 + x)) = 28
((7 * -5 + x * -5) + x(7 + x)) = 28
((-35 + -5x) + x(7 + x)) = 28
(-35 + -5x + (7 * x + x * x)) = 28
(-35 + -5x + (7x + x2)) = 28

Combine like terms: -5x + 7x = 2x
(-35 + 2x + x2) = 28

Solving
-35 + 2x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
-35 + -28 + 2x + x2 = 28 + -28

Combine like terms: -35 + -28 = -63
-63 + 2x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-63 + 2x + x2 = 0

Factor a trinomial.
(-9 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
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
Solution
x = {-9, 7}

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