(x+1)(x+4)=3x+39

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Solution for (x+1)(x+4)=3x+39 equation: 


Simplifying
(x + 1)(x + 4) = 3x + 39

Reorder the terms:
(1 + x)(x + 4) = 3x + 39

Reorder the terms:
(1 + x)(4 + x) = 3x + 39

Multiply (1 + x) * (4 + x)
(1(4 + x) + x(4 + x)) = 3x + 39
((4 * 1 + x * 1) + x(4 + x)) = 3x + 39
((4 + 1x) + x(4 + x)) = 3x + 39
(4 + 1x + (4 * x + x * x)) = 3x + 39
(4 + 1x + (4x + x2)) = 3x + 39

Combine like terms: 1x + 4x = 5x
(4 + 5x + x2) = 3x + 39

Reorder the terms:
4 + 5x + x2 = 39 + 3x

Solving
4 + 5x + x2 = 39 + 3x

Solving for variable 'x'.

Reorder the terms:
4 + -39 + 5x + -3x + x2 = 39 + 3x + -39 + -3x

Combine like terms: 4 + -39 = -35
-35 + 5x + -3x + x2 = 39 + 3x + -39 + -3x

Combine like terms: 5x + -3x = 2x
-35 + 2x + x2 = 39 + 3x + -39 + -3x

Reorder the terms:
-35 + 2x + x2 = 39 + -39 + 3x + -3x

Combine like terms: 39 + -39 = 0
-35 + 2x + x2 = 0 + 3x + -3x
-35 + 2x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-35 + 2x + x2 = 0

Factor a trinomial.
(-7 + -1x)(5 + -1x) = 0


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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-7, 5}

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