(x+5)(x-2)=30

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Solution for (x+5)(x-2)=30 equation: 


Simplifying
(x + 5)(x + -2) = 30

Reorder the terms:
(5 + x)(x + -2) = 30

Reorder the terms:
(5 + x)(-2 + x) = 30

Multiply (5 + x) * (-2 + x)
(5(-2 + x) + x(-2 + x)) = 30
((-2 * 5 + x * 5) + x(-2 + x)) = 30
((-10 + 5x) + x(-2 + x)) = 30
(-10 + 5x + (-2 * x + x * x)) = 30
(-10 + 5x + (-2x + x2)) = 30

Combine like terms: 5x + -2x = 3x
(-10 + 3x + x2) = 30

Solving
-10 + 3x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
-10 + -30 + 3x + x2 = 30 + -30

Combine like terms: -10 + -30 = -40
-40 + 3x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-40 + 3x + x2 = 0

Factor a trinomial.
(-8 + -1x)(5 + -1x) = 0


Subproblem 1
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

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 = {-8, 5}

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