(x+3)(2x-5)+(2x-5)2=0

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Solution for (x+3)(2x-5)+(2x-5)2=0 equation:


Simplifying
(x + 3)(2x + -5) + (2x + -5) * 2 = 0

Reorder the terms:
(3 + x)(2x + -5) + (2x + -5) * 2 = 0

Reorder the terms:
(3 + x)(-5 + 2x) + (2x + -5) * 2 = 0

Multiply (3 + x) * (-5 + 2x)
(3(-5 + 2x) + x(-5 + 2x)) + (2x + -5) * 2 = 0
((-5 * 3 + 2x * 3) + x(-5 + 2x)) + (2x + -5) * 2 = 0
((-15 + 6x) + x(-5 + 2x)) + (2x + -5) * 2 = 0
(-15 + 6x + (-5 * x + 2x * x)) + (2x + -5) * 2 = 0
(-15 + 6x + (-5x + 2x2)) + (2x + -5) * 2 = 0

Combine like terms: 6x + -5x = 1x
(-15 + 1x + 2x2) + (2x + -5) * 2 = 0

Reorder the terms:
-15 + 1x + 2x2 + (-5 + 2x) * 2 = 0

Reorder the terms for easier multiplication:
-15 + 1x + 2x2 + 2(-5 + 2x) = 0
-15 + 1x + 2x2 + (-5 * 2 + 2x * 2) = 0
-15 + 1x + 2x2 + (-10 + 4x) = 0

Reorder the terms:
-15 + -10 + 1x + 4x + 2x2 = 0

Combine like terms: -15 + -10 = -25
-25 + 1x + 4x + 2x2 = 0

Combine like terms: 1x + 4x = 5x
-25 + 5x + 2x2 = 0

Solving
-25 + 5x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x)(5 + -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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-5, 2.5}

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