4x(x+5)=(3x-9)(x+5)

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Solution for 4x(x+5)=(3x-9)(x+5) equation: 


Simplifying
4x(x + 5) = (3x + -9)(x + 5)

Reorder the terms:
4x(5 + x) = (3x + -9)(x + 5)
(5 * 4x + x * 4x) = (3x + -9)(x + 5)
(20x + 4x2) = (3x + -9)(x + 5)

Reorder the terms:
20x + 4x2 = (-9 + 3x)(x + 5)

Reorder the terms:
20x + 4x2 = (-9 + 3x)(5 + x)

Multiply (-9 + 3x) * (5 + x)
20x + 4x2 = (-9(5 + x) + 3x * (5 + x))
20x + 4x2 = ((5 * -9 + x * -9) + 3x * (5 + x))
20x + 4x2 = ((-45 + -9x) + 3x * (5 + x))
20x + 4x2 = (-45 + -9x + (5 * 3x + x * 3x))
20x + 4x2 = (-45 + -9x + (15x + 3x2))

Combine like terms: -9x + 15x = 6x
20x + 4x2 = (-45 + 6x + 3x2)

Solving
20x + 4x2 = -45 + 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
45 + 20x + -6x + 4x2 + -3x2 = -45 + 6x + 3x2 + 45 + -6x + -3x2

Combine like terms: 20x + -6x = 14x
45 + 14x + 4x2 + -3x2 = -45 + 6x + 3x2 + 45 + -6x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
45 + 14x + 1x2 = -45 + 6x + 3x2 + 45 + -6x + -3x2

Reorder the terms:
45 + 14x + 1x2 = -45 + 45 + 6x + -6x + 3x2 + -3x2

Combine like terms: -45 + 45 = 0
45 + 14x + 1x2 = 0 + 6x + -6x + 3x2 + -3x2
45 + 14x + 1x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
45 + 14x + 1x2 = 0 + 3x2 + -3x2
45 + 14x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
45 + 14x + 1x2 = 0

Factor a trinomial.
(9 + x)(5 + x) = 0


Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9

Subproblem 2
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
Solution
x = {-9, -5}

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