(4x+12)(x+3)=(x-7)(x+3)

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Solution for (4x+12)(x+3)=(x-7)(x+3) equation: 


Simplifying
(4x + 12)(x + 3) = (x + -7)(x + 3)

Reorder the terms:
(12 + 4x)(x + 3) = (x + -7)(x + 3)

Reorder the terms:
(12 + 4x)(3 + x) = (x + -7)(x + 3)

Multiply (12 + 4x) * (3 + x)
(12(3 + x) + 4x * (3 + x)) = (x + -7)(x + 3)
((3 * 12 + x * 12) + 4x * (3 + x)) = (x + -7)(x + 3)
((36 + 12x) + 4x * (3 + x)) = (x + -7)(x + 3)
(36 + 12x + (3 * 4x + x * 4x)) = (x + -7)(x + 3)
(36 + 12x + (12x + 4x2)) = (x + -7)(x + 3)

Combine like terms: 12x + 12x = 24x
(36 + 24x + 4x2) = (x + -7)(x + 3)

Reorder the terms:
36 + 24x + 4x2 = (-7 + x)(x + 3)

Reorder the terms:
36 + 24x + 4x2 = (-7 + x)(3 + x)

Multiply (-7 + x) * (3 + x)
36 + 24x + 4x2 = (-7(3 + x) + x(3 + x))
36 + 24x + 4x2 = ((3 * -7 + x * -7) + x(3 + x))
36 + 24x + 4x2 = ((-21 + -7x) + x(3 + x))
36 + 24x + 4x2 = (-21 + -7x + (3 * x + x * x))
36 + 24x + 4x2 = (-21 + -7x + (3x + x2))

Combine like terms: -7x + 3x = -4x
36 + 24x + 4x2 = (-21 + -4x + x2)

Solving
36 + 24x + 4x2 = -21 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
36 + 21 + 24x + 4x + 4x2 + -1x2 = -21 + -4x + x2 + 21 + 4x + -1x2

Combine like terms: 36 + 21 = 57
57 + 24x + 4x + 4x2 + -1x2 = -21 + -4x + x2 + 21 + 4x + -1x2

Combine like terms: 24x + 4x = 28x
57 + 28x + 4x2 + -1x2 = -21 + -4x + x2 + 21 + 4x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
57 + 28x + 3x2 = -21 + -4x + x2 + 21 + 4x + -1x2

Reorder the terms:
57 + 28x + 3x2 = -21 + 21 + -4x + 4x + x2 + -1x2

Combine like terms: -21 + 21 = 0
57 + 28x + 3x2 = 0 + -4x + 4x + x2 + -1x2
57 + 28x + 3x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
57 + 28x + 3x2 = 0 + x2 + -1x2
57 + 28x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
57 + 28x + 3x2 = 0

Factor a trinomial.
(19 + 3x)(3 + x) = 0


Subproblem 1
Set the factor '(19 + 3x)' equal to zero and attempt to solve:

Simplifying
19 + 3x = 0

Solving
19 + 3x = 0

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

Add '-19' to each side of the equation.
19 + -19 + 3x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 3x = 0 + -19
3x = 0 + -19

Combine like terms: 0 + -19 = -19
3x = -19

Divide each side by '3'.
x = -6.333333333

Simplifying
x = -6.333333333

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 = {-6.333333333, -3}

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