(2x+5)(3x+4)+1=0

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Solution for (2x+5)(3x+4)+1=0 equation: 


Simplifying
(2x + 5)(3x + 4) + 1 = 0

Reorder the terms:
(5 + 2x)(3x + 4) + 1 = 0

Reorder the terms:
(5 + 2x)(4 + 3x) + 1 = 0

Multiply (5 + 2x) * (4 + 3x)
(5(4 + 3x) + 2x * (4 + 3x)) + 1 = 0
((4 * 5 + 3x * 5) + 2x * (4 + 3x)) + 1 = 0
((20 + 15x) + 2x * (4 + 3x)) + 1 = 0
(20 + 15x + (4 * 2x + 3x * 2x)) + 1 = 0
(20 + 15x + (8x + 6x2)) + 1 = 0

Combine like terms: 15x + 8x = 23x
(20 + 23x + 6x2) + 1 = 0

Reorder the terms:
20 + 1 + 23x + 6x2 = 0

Combine like terms: 20 + 1 = 21
21 + 23x + 6x2 = 0

Solving
21 + 23x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + 3x)(3 + 2x) = 0


Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-2.333333333, -1.5}

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