(x-7)(x+5)=-20

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Solution for (x-7)(x+5)=-20 equation: 


Simplifying
(x + -7)(x + 5) = -20

Reorder the terms:
(-7 + x)(x + 5) = -20

Reorder the terms:
(-7 + x)(5 + x) = -20

Multiply (-7 + x) * (5 + x)
(-7(5 + x) + x(5 + x)) = -20
((5 * -7 + x * -7) + x(5 + x)) = -20
((-35 + -7x) + x(5 + x)) = -20
(-35 + -7x + (5 * x + x * x)) = -20
(-35 + -7x + (5x + x2)) = -20

Combine like terms: -7x + 5x = -2x
(-35 + -2x + x2) = -20

Solving
-35 + -2x + x2 = -20

Solving for variable 'x'.

Reorder the terms:
-35 + 20 + -2x + x2 = -20 + 20

Combine like terms: -35 + 20 = -15
-15 + -2x + x2 = -20 + 20

Combine like terms: -20 + 20 = 0
-15 + -2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}

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