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

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


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

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

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

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

Combine like terms: 4x + 15x = 19x
(10 + 19x + 6x2) = -4

Solving
10 + 19x + 6x2 = -4

Solving for variable 'x'.

Reorder the terms:
10 + 4 + 19x + 6x2 = -4 + 4

Combine like terms: 10 + 4 = 14
14 + 19x + 6x2 = -4 + 4

Combine like terms: -4 + 4 = 0
14 + 19x + 6x2 = 0

Factor a trinomial.
(2 + x)(7 + 6x) = 0


Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(7 + 6x)' equal to zero and attempt to solve:

Simplifying
7 + 6x = 0

Solving
7 + 6x = 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 + 6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6x = 0 + -7
6x = 0 + -7

Combine like terms: 0 + -7 = -7
6x = -7

Divide each side by '6'.
x = -1.166666667

Simplifying
x = -1.166666667
Solution
x = {-2, -1.166666667}

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