(2x+5)(x-3)=30

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Solution for (2x+5)(x-3)=30 equation: 


Simplifying
(2x + 5)(x + -3) = 30

Reorder the terms:
(5 + 2x)(x + -3) = 30

Reorder the terms:
(5 + 2x)(-3 + x) = 30

Multiply (5 + 2x) * (-3 + x)
(5(-3 + x) + 2x * (-3 + x)) = 30
((-3 * 5 + x * 5) + 2x * (-3 + x)) = 30
((-15 + 5x) + 2x * (-3 + x)) = 30
(-15 + 5x + (-3 * 2x + x * 2x)) = 30
(-15 + 5x + (-6x + 2x2)) = 30

Combine like terms: 5x + -6x = -1x
(-15 + -1x + 2x2) = 30

Solving
-15 + -1x + 2x2 = 30

Solving for variable 'x'.

Reorder the terms:
-15 + -30 + -1x + 2x2 = 30 + -30

Combine like terms: -15 + -30 = -45
-45 + -1x + 2x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-45 + -1x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 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 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

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 = {-4.5, 5}

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