(2x+5)(2x+5)+(2x+5)(x-4)+3(2x+5)=0

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Solution for (2x+5)(2x+5)+(2x+5)(x-4)+3(2x+5)=0 equation: 


Simplifying
(2x + 5)(2x + 5) + (2x + 5)(x + -4) + 3(2x + 5) = 0

Reorder the terms:
(5 + 2x)(2x + 5) + (2x + 5)(x + -4) + 3(2x + 5) = 0

Reorder the terms:
(5 + 2x)(5 + 2x) + (2x + 5)(x + -4) + 3(2x + 5) = 0

Multiply (5 + 2x) * (5 + 2x)
(5(5 + 2x) + 2x * (5 + 2x)) + (2x + 5)(x + -4) + 3(2x + 5) = 0
((5 * 5 + 2x * 5) + 2x * (5 + 2x)) + (2x + 5)(x + -4) + 3(2x + 5) = 0
((25 + 10x) + 2x * (5 + 2x)) + (2x + 5)(x + -4) + 3(2x + 5) = 0
(25 + 10x + (5 * 2x + 2x * 2x)) + (2x + 5)(x + -4) + 3(2x + 5) = 0
(25 + 10x + (10x + 4x2)) + (2x + 5)(x + -4) + 3(2x + 5) = 0

Combine like terms: 10x + 10x = 20x
(25 + 20x + 4x2) + (2x + 5)(x + -4) + 3(2x + 5) = 0

Reorder the terms:
25 + 20x + 4x2 + (5 + 2x)(x + -4) + 3(2x + 5) = 0

Reorder the terms:
25 + 20x + 4x2 + (5 + 2x)(-4 + x) + 3(2x + 5) = 0

Multiply (5 + 2x) * (-4 + x)
25 + 20x + 4x2 + (5(-4 + x) + 2x * (-4 + x)) + 3(2x + 5) = 0
25 + 20x + 4x2 + ((-4 * 5 + x * 5) + 2x * (-4 + x)) + 3(2x + 5) = 0
25 + 20x + 4x2 + ((-20 + 5x) + 2x * (-4 + x)) + 3(2x + 5) = 0
25 + 20x + 4x2 + (-20 + 5x + (-4 * 2x + x * 2x)) + 3(2x + 5) = 0
25 + 20x + 4x2 + (-20 + 5x + (-8x + 2x2)) + 3(2x + 5) = 0

Combine like terms: 5x + -8x = -3x
25 + 20x + 4x2 + (-20 + -3x + 2x2) + 3(2x + 5) = 0

Reorder the terms:
25 + 20x + 4x2 + -20 + -3x + 2x2 + 3(5 + 2x) = 0
25 + 20x + 4x2 + -20 + -3x + 2x2 + (5 * 3 + 2x * 3) = 0
25 + 20x + 4x2 + -20 + -3x + 2x2 + (15 + 6x) = 0

Reorder the terms:
25 + -20 + 15 + 20x + -3x + 6x + 4x2 + 2x2 = 0

Combine like terms: 25 + -20 = 5
5 + 15 + 20x + -3x + 6x + 4x2 + 2x2 = 0

Combine like terms: 5 + 15 = 20
20 + 20x + -3x + 6x + 4x2 + 2x2 = 0

Combine like terms: 20x + -3x = 17x
20 + 17x + 6x + 4x2 + 2x2 = 0

Combine like terms: 17x + 6x = 23x
20 + 23x + 4x2 + 2x2 = 0

Combine like terms: 4x2 + 2x2 = 6x2
20 + 23x + 6x2 = 0

Solving
20 + 23x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + 2x)(4 + 3x) = 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 '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {-2.5, -1.333333333}

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