(x-8)(x+5)=30

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Solution for (x-8)(x+5)=30 equation: 


Simplifying
(x + -8)(x + 5) = 30

Reorder the terms:
(-8 + x)(x + 5) = 30

Reorder the terms:
(-8 + x)(5 + x) = 30

Multiply (-8 + x) * (5 + x)
(-8(5 + x) + x(5 + x)) = 30
((5 * -8 + x * -8) + x(5 + x)) = 30
((-40 + -8x) + x(5 + x)) = 30
(-40 + -8x + (5 * x + x * x)) = 30
(-40 + -8x + (5x + x2)) = 30

Combine like terms: -8x + 5x = -3x
(-40 + -3x + x2) = 30

Solving
-40 + -3x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
-40 + -30 + -3x + x2 = 30 + -30

Combine like terms: -40 + -30 = -70
-70 + -3x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-70 + -3x + x2 = 0

Factor a trinomial.
(-7 + -1x)(10 + -1x) = 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 '(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
Solution
x = {-7, 10}

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