(x+5)(2x-1)=40

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Solution for (x+5)(2x-1)=40 equation: 


Simplifying
(x + 5)(2x + -1) = 40

Reorder the terms:
(5 + x)(2x + -1) = 40

Reorder the terms:
(5 + x)(-1 + 2x) = 40

Multiply (5 + x) * (-1 + 2x)
(5(-1 + 2x) + x(-1 + 2x)) = 40
((-1 * 5 + 2x * 5) + x(-1 + 2x)) = 40
((-5 + 10x) + x(-1 + 2x)) = 40
(-5 + 10x + (-1 * x + 2x * x)) = 40
(-5 + 10x + (-1x + 2x2)) = 40

Combine like terms: 10x + -1x = 9x
(-5 + 9x + 2x2) = 40

Solving
-5 + 9x + 2x2 = 40

Solving for variable 'x'.

Reorder the terms:
-5 + -40 + 9x + 2x2 = 40 + -40

Combine like terms: -5 + -40 = -45
-45 + 9x + 2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-45 + 9x + 2x2 = 0

Factor a trinomial.
(-15 + -2x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve:

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-7.5, 3}

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