(x+5)(4x+3)=-13

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Solution for (x+5)(4x+3)=-13 equation: 


Simplifying
(x + 5)(4x + 3) = -13

Reorder the terms:
(5 + x)(4x + 3) = -13

Reorder the terms:
(5 + x)(3 + 4x) = -13

Multiply (5 + x) * (3 + 4x)
(5(3 + 4x) + x(3 + 4x)) = -13
((3 * 5 + 4x * 5) + x(3 + 4x)) = -13
((15 + 20x) + x(3 + 4x)) = -13
(15 + 20x + (3 * x + 4x * x)) = -13
(15 + 20x + (3x + 4x2)) = -13

Combine like terms: 20x + 3x = 23x
(15 + 23x + 4x2) = -13

Solving
15 + 23x + 4x2 = -13

Solving for variable 'x'.

Reorder the terms:
15 + 13 + 23x + 4x2 = -13 + 13

Combine like terms: 15 + 13 = 28
28 + 23x + 4x2 = -13 + 13

Combine like terms: -13 + 13 = 0
28 + 23x + 4x2 = 0

Factor a trinomial.
(4 + x)(7 + 4x) = 0


Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4

Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 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 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75
Solution
x = {-4, -1.75}

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