(2x+5)(x-3)=40

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Solution for (2x+5)(x-3)=40 equation: 


Simplifying
(2x + 5)(x + -3) = 40

Reorder the terms:
(5 + 2x)(x + -3) = 40

Reorder the terms:
(5 + 2x)(-3 + x) = 40

Multiply (5 + 2x) * (-3 + x)
(5(-3 + x) + 2x * (-3 + x)) = 40
((-3 * 5 + x * 5) + 2x * (-3 + x)) = 40
((-15 + 5x) + 2x * (-3 + x)) = 40
(-15 + 5x + (-3 * 2x + x * 2x)) = 40
(-15 + 5x + (-6x + 2x2)) = 40

Combine like terms: 5x + -6x = -1x
(-15 + -1x + 2x2) = 40

Solving
-15 + -1x + 2x2 = 40

Solving for variable 'x'.

Reorder the terms:
-15 + -40 + -1x + 2x2 = 40 + -40

Combine like terms: -15 + -40 = -55
-55 + -1x + 2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-55 + -1x + 2x2 = 0

Factor a trinomial.
(-5 + -1x)(11 + -2x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {-5, 5.5}

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