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

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


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

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

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

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

Combine like terms: 6x + -5x = 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.
(-11 + -2x)(5 + -1x) = 0


Subproblem 1
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

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 = {-5.5, 5}

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