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

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Solution for (2x+5)(x+1)-(2x+5)(2x-3)=0 equation: 


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

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

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

Multiply (5 + 2x) * (1 + x)
(5(1 + x) + 2x * (1 + x)) + -1(2x + 5)(2x + -3) = 0
((1 * 5 + x * 5) + 2x * (1 + x)) + -1(2x + 5)(2x + -3) = 0
((5 + 5x) + 2x * (1 + x)) + -1(2x + 5)(2x + -3) = 0
(5 + 5x + (1 * 2x + x * 2x)) + -1(2x + 5)(2x + -3) = 0
(5 + 5x + (2x + 2x2)) + -1(2x + 5)(2x + -3) = 0

Combine like terms: 5x + 2x = 7x
(5 + 7x + 2x2) + -1(2x + 5)(2x + -3) = 0

Reorder the terms:
5 + 7x + 2x2 + -1(5 + 2x)(2x + -3) = 0

Reorder the terms:
5 + 7x + 2x2 + -1(5 + 2x)(-3 + 2x) = 0

Multiply (5 + 2x) * (-3 + 2x)
5 + 7x + 2x2 + -1(5(-3 + 2x) + 2x * (-3 + 2x)) = 0
5 + 7x + 2x2 + -1((-3 * 5 + 2x * 5) + 2x * (-3 + 2x)) = 0
5 + 7x + 2x2 + -1((-15 + 10x) + 2x * (-3 + 2x)) = 0
5 + 7x + 2x2 + -1(-15 + 10x + (-3 * 2x + 2x * 2x)) = 0
5 + 7x + 2x2 + -1(-15 + 10x + (-6x + 4x2)) = 0

Combine like terms: 10x + -6x = 4x
5 + 7x + 2x2 + -1(-15 + 4x + 4x2) = 0
5 + 7x + 2x2 + (-15 * -1 + 4x * -1 + 4x2 * -1) = 0
5 + 7x + 2x2 + (15 + -4x + -4x2) = 0

Reorder the terms:
5 + 15 + 7x + -4x + 2x2 + -4x2 = 0

Combine like terms: 5 + 15 = 20
20 + 7x + -4x + 2x2 + -4x2 = 0

Combine like terms: 7x + -4x = 3x
20 + 3x + 2x2 + -4x2 = 0

Combine like terms: 2x2 + -4x2 = -2x2
20 + 3x + -2x2 = 0

Solving
20 + 3x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(5 + 2x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -2.5}

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