(x+4)(5x+2)=-13

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Solution for (x+4)(5x+2)=-13 equation: 


Simplifying
(x + 4)(5x + 2) = -13

Reorder the terms:
(4 + x)(5x + 2) = -13

Reorder the terms:
(4 + x)(2 + 5x) = -13

Multiply (4 + x) * (2 + 5x)
(4(2 + 5x) + x(2 + 5x)) = -13
((2 * 4 + 5x * 4) + x(2 + 5x)) = -13
((8 + 20x) + x(2 + 5x)) = -13
(8 + 20x + (2 * x + 5x * x)) = -13
(8 + 20x + (2x + 5x2)) = -13

Combine like terms: 20x + 2x = 22x
(8 + 22x + 5x2) = -13

Solving
8 + 22x + 5x2 = -13

Solving for variable 'x'.

Reorder the terms:
8 + 13 + 22x + 5x2 = -13 + 13

Combine like terms: 8 + 13 = 21
21 + 22x + 5x2 = -13 + 13

Combine like terms: -13 + 13 = 0
21 + 22x + 5x2 = 0

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


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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3

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 = {-3, -1.4}

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