9x+25=(x+1)(x+4)

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Solution for 9x+25=(x+1)(x+4) equation: 


Simplifying
9x + 25 = (x + 1)(x + 4)

Reorder the terms:
25 + 9x = (x + 1)(x + 4)

Reorder the terms:
25 + 9x = (1 + x)(x + 4)

Reorder the terms:
25 + 9x = (1 + x)(4 + x)

Multiply (1 + x) * (4 + x)
25 + 9x = (1(4 + x) + x(4 + x))
25 + 9x = ((4 * 1 + x * 1) + x(4 + x))
25 + 9x = ((4 + 1x) + x(4 + x))
25 + 9x = (4 + 1x + (4 * x + x * x))
25 + 9x = (4 + 1x + (4x + x2))

Combine like terms: 1x + 4x = 5x
25 + 9x = (4 + 5x + x2)

Solving
25 + 9x = 4 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
25 + -4 + 9x + -5x + -1x2 = 4 + 5x + x2 + -4 + -5x + -1x2

Combine like terms: 25 + -4 = 21
21 + 9x + -5x + -1x2 = 4 + 5x + x2 + -4 + -5x + -1x2

Combine like terms: 9x + -5x = 4x
21 + 4x + -1x2 = 4 + 5x + x2 + -4 + -5x + -1x2

Reorder the terms:
21 + 4x + -1x2 = 4 + -4 + 5x + -5x + x2 + -1x2

Combine like terms: 4 + -4 = 0
21 + 4x + -1x2 = 0 + 5x + -5x + x2 + -1x2
21 + 4x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
21 + 4x + -1x2 = 0 + x2 + -1x2
21 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21 + 4x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(3 + x) = 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 '(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
Solution
x = {7, -3}

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