(x+1)(2x+4)=7(3x-3)

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Solution for (x+1)(2x+4)=7(3x-3) equation: 


Simplifying
(x + 1)(2x + 4) = 7(3x + -3)

Reorder the terms:
(1 + x)(2x + 4) = 7(3x + -3)

Reorder the terms:
(1 + x)(4 + 2x) = 7(3x + -3)

Multiply (1 + x) * (4 + 2x)
(1(4 + 2x) + x(4 + 2x)) = 7(3x + -3)
((4 * 1 + 2x * 1) + x(4 + 2x)) = 7(3x + -3)
((4 + 2x) + x(4 + 2x)) = 7(3x + -3)
(4 + 2x + (4 * x + 2x * x)) = 7(3x + -3)
(4 + 2x + (4x + 2x2)) = 7(3x + -3)

Combine like terms: 2x + 4x = 6x
(4 + 6x + 2x2) = 7(3x + -3)

Reorder the terms:
4 + 6x + 2x2 = 7(-3 + 3x)
4 + 6x + 2x2 = (-3 * 7 + 3x * 7)
4 + 6x + 2x2 = (-21 + 21x)

Solving
4 + 6x + 2x2 = -21 + 21x

Solving for variable 'x'.

Reorder the terms:
4 + 21 + 6x + -21x + 2x2 = -21 + 21x + 21 + -21x

Combine like terms: 4 + 21 = 25
25 + 6x + -21x + 2x2 = -21 + 21x + 21 + -21x

Combine like terms: 6x + -21x = -15x
25 + -15x + 2x2 = -21 + 21x + 21 + -21x

Reorder the terms:
25 + -15x + 2x2 = -21 + 21 + 21x + -21x

Combine like terms: -21 + 21 = 0
25 + -15x + 2x2 = 0 + 21x + -21x
25 + -15x + 2x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
25 + -15x + 2x2 = 0

Factor a trinomial.
(5 + -2x)(5 + -1x) = 0


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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

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 = {2.5, 5}

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