(2x+3)(5-2x)+(5-2x)(9-x)=0

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Solution for (2x+3)(5-2x)+(5-2x)(9-x)=0 equation: 


Simplifying
(2x + 3)(5 + -2x) + (5 + -2x)(9 + -1x) = 0

Reorder the terms:
(3 + 2x)(5 + -2x) + (5 + -2x)(9 + -1x) = 0

Multiply (3 + 2x) * (5 + -2x)
(3(5 + -2x) + 2x * (5 + -2x)) + (5 + -2x)(9 + -1x) = 0
((5 * 3 + -2x * 3) + 2x * (5 + -2x)) + (5 + -2x)(9 + -1x) = 0
((15 + -6x) + 2x * (5 + -2x)) + (5 + -2x)(9 + -1x) = 0
(15 + -6x + (5 * 2x + -2x * 2x)) + (5 + -2x)(9 + -1x) = 0
(15 + -6x + (10x + -4x2)) + (5 + -2x)(9 + -1x) = 0

Combine like terms: -6x + 10x = 4x
(15 + 4x + -4x2) + (5 + -2x)(9 + -1x) = 0

Multiply (5 + -2x) * (9 + -1x)
15 + 4x + -4x2 + (5(9 + -1x) + -2x * (9 + -1x)) = 0
15 + 4x + -4x2 + ((9 * 5 + -1x * 5) + -2x * (9 + -1x)) = 0
15 + 4x + -4x2 + ((45 + -5x) + -2x * (9 + -1x)) = 0
15 + 4x + -4x2 + (45 + -5x + (9 * -2x + -1x * -2x)) = 0
15 + 4x + -4x2 + (45 + -5x + (-18x + 2x2)) = 0

Combine like terms: -5x + -18x = -23x
15 + 4x + -4x2 + (45 + -23x + 2x2) = 0

Reorder the terms:
15 + 45 + 4x + -23x + -4x2 + 2x2 = 0

Combine like terms: 15 + 45 = 60
60 + 4x + -23x + -4x2 + 2x2 = 0

Combine like terms: 4x + -23x = -19x
60 + -19x + -4x2 + 2x2 = 0

Combine like terms: -4x2 + 2x2 = -2x2
60 + -19x + -2x2 = 0

Solving
60 + -19x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -2x)(12 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {2.5, -12}

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