-4(x+2)-9(x+4)=7(x+2)(x+4)

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Solution for -4(x+2)-9(x+4)=7(x+2)(x+4) equation: 


Simplifying
-4(x + 2) + -9(x + 4) = 7(x + 2)(x + 4)

Reorder the terms:
-4(2 + x) + -9(x + 4) = 7(x + 2)(x + 4)
(2 * -4 + x * -4) + -9(x + 4) = 7(x + 2)(x + 4)
(-8 + -4x) + -9(x + 4) = 7(x + 2)(x + 4)

Reorder the terms:
-8 + -4x + -9(4 + x) = 7(x + 2)(x + 4)
-8 + -4x + (4 * -9 + x * -9) = 7(x + 2)(x + 4)
-8 + -4x + (-36 + -9x) = 7(x + 2)(x + 4)

Reorder the terms:
-8 + -36 + -4x + -9x = 7(x + 2)(x + 4)

Combine like terms: -8 + -36 = -44
-44 + -4x + -9x = 7(x + 2)(x + 4)

Combine like terms: -4x + -9x = -13x
-44 + -13x = 7(x + 2)(x + 4)

Reorder the terms:
-44 + -13x = 7(2 + x)(x + 4)

Reorder the terms:
-44 + -13x = 7(2 + x)(4 + x)

Multiply (2 + x) * (4 + x)
-44 + -13x = 7(2(4 + x) + x(4 + x))
-44 + -13x = 7((4 * 2 + x * 2) + x(4 + x))
-44 + -13x = 7((8 + 2x) + x(4 + x))
-44 + -13x = 7(8 + 2x + (4 * x + x * x))
-44 + -13x = 7(8 + 2x + (4x + x2))

Combine like terms: 2x + 4x = 6x
-44 + -13x = 7(8 + 6x + x2)
-44 + -13x = (8 * 7 + 6x * 7 + x2 * 7)
-44 + -13x = (56 + 42x + 7x2)

Solving
-44 + -13x = 56 + 42x + 7x2

Solving for variable 'x'.

Reorder the terms:
-44 + -56 + -13x + -42x + -7x2 = 56 + 42x + 7x2 + -56 + -42x + -7x2

Combine like terms: -44 + -56 = -100
-100 + -13x + -42x + -7x2 = 56 + 42x + 7x2 + -56 + -42x + -7x2

Combine like terms: -13x + -42x = -55x
-100 + -55x + -7x2 = 56 + 42x + 7x2 + -56 + -42x + -7x2

Reorder the terms:
-100 + -55x + -7x2 = 56 + -56 + 42x + -42x + 7x2 + -7x2

Combine like terms: 56 + -56 = 0
-100 + -55x + -7x2 = 0 + 42x + -42x + 7x2 + -7x2
-100 + -55x + -7x2 = 42x + -42x + 7x2 + -7x2

Combine like terms: 42x + -42x = 0
-100 + -55x + -7x2 = 0 + 7x2 + -7x2
-100 + -55x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-100 + -55x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(100 + 55x + 7x2) = 0

Factor a trinomial.
-1((5 + x)(20 + 7x)) = 0

Ignore the factor -1.

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

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5

Subproblem 2
Set the factor '(20 + 7x)' equal to zero and attempt to solve:

Simplifying
20 + 7x = 0

Solving
20 + 7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-20' to each side of the equation.
20 + -20 + 7x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 7x = 0 + -20
7x = 0 + -20

Combine like terms: 0 + -20 = -20
7x = -20

Divide each side by '7'.
x = -2.857142857

Simplifying
x = -2.857142857
Solution
x = {-5, -2.857142857}

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