(x+6)(5x+2)=-23

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Solution for (x+6)(5x+2)=-23 equation: 


Simplifying
(x + 6)(5x + 2) = -23

Reorder the terms:
(6 + x)(5x + 2) = -23

Reorder the terms:
(6 + x)(2 + 5x) = -23

Multiply (6 + x) * (2 + 5x)
(6(2 + 5x) + x(2 + 5x)) = -23
((2 * 6 + 5x * 6) + x(2 + 5x)) = -23
((12 + 30x) + x(2 + 5x)) = -23
(12 + 30x + (2 * x + 5x * x)) = -23
(12 + 30x + (2x + 5x2)) = -23

Combine like terms: 30x + 2x = 32x
(12 + 32x + 5x2) = -23

Solving
12 + 32x + 5x2 = -23

Solving for variable 'x'.

Reorder the terms:
12 + 23 + 32x + 5x2 = -23 + 23

Combine like terms: 12 + 23 = 35
35 + 32x + 5x2 = -23 + 23

Combine like terms: -23 + 23 = 0
35 + 32x + 5x2 = 0

Factor a trinomial.
(5 + x)(7 + 5x) = 0


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(7 + 5x)' equal to zero and attempt to solve:

Simplifying
7 + 5x = 0

Solving
7 + 5x = 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 + 5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5x = 0 + -7
5x = 0 + -7

Combine like terms: 0 + -7 = -7
5x = -7

Divide each side by '5'.
x = -1.4

Simplifying
x = -1.4
Solution
x = {-5, -1.4}

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