(x+7)(x-5)=45

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Solution for (x+7)(x-5)=45 equation: 


Simplifying
(x + 7)(x + -5) = 45

Reorder the terms:
(7 + x)(x + -5) = 45

Reorder the terms:
(7 + x)(-5 + x) = 45

Multiply (7 + x) * (-5 + x)
(7(-5 + x) + x(-5 + x)) = 45
((-5 * 7 + x * 7) + x(-5 + x)) = 45
((-35 + 7x) + x(-5 + x)) = 45
(-35 + 7x + (-5 * x + x * x)) = 45
(-35 + 7x + (-5x + x2)) = 45

Combine like terms: 7x + -5x = 2x
(-35 + 2x + x2) = 45

Solving
-35 + 2x + x2 = 45

Solving for variable 'x'.

Reorder the terms:
-35 + -45 + 2x + x2 = 45 + -45

Combine like terms: -35 + -45 = -80
-80 + 2x + x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-80 + 2x + x2 = 0

Factor a trinomial.
(-10 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-10, 8}

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