(5x+2)(6x+14)=(7x+3)(3x+9)

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Solution for (5x+2)(6x+14)=(7x+3)(3x+9) equation: 


Simplifying
(5x + 2)(6x + 14) = (7x + 3)(3x + 9)

Reorder the terms:
(2 + 5x)(6x + 14) = (7x + 3)(3x + 9)

Reorder the terms:
(2 + 5x)(14 + 6x) = (7x + 3)(3x + 9)

Multiply (2 + 5x) * (14 + 6x)
(2(14 + 6x) + 5x * (14 + 6x)) = (7x + 3)(3x + 9)
((14 * 2 + 6x * 2) + 5x * (14 + 6x)) = (7x + 3)(3x + 9)
((28 + 12x) + 5x * (14 + 6x)) = (7x + 3)(3x + 9)
(28 + 12x + (14 * 5x + 6x * 5x)) = (7x + 3)(3x + 9)
(28 + 12x + (70x + 30x2)) = (7x + 3)(3x + 9)

Combine like terms: 12x + 70x = 82x
(28 + 82x + 30x2) = (7x + 3)(3x + 9)

Reorder the terms:
28 + 82x + 30x2 = (3 + 7x)(3x + 9)

Reorder the terms:
28 + 82x + 30x2 = (3 + 7x)(9 + 3x)

Multiply (3 + 7x) * (9 + 3x)
28 + 82x + 30x2 = (3(9 + 3x) + 7x * (9 + 3x))
28 + 82x + 30x2 = ((9 * 3 + 3x * 3) + 7x * (9 + 3x))
28 + 82x + 30x2 = ((27 + 9x) + 7x * (9 + 3x))
28 + 82x + 30x2 = (27 + 9x + (9 * 7x + 3x * 7x))
28 + 82x + 30x2 = (27 + 9x + (63x + 21x2))

Combine like terms: 9x + 63x = 72x
28 + 82x + 30x2 = (27 + 72x + 21x2)

Solving
28 + 82x + 30x2 = 27 + 72x + 21x2

Solving for variable 'x'.

Reorder the terms:
28 + -27 + 82x + -72x + 30x2 + -21x2 = 27 + 72x + 21x2 + -27 + -72x + -21x2

Combine like terms: 28 + -27 = 1
1 + 82x + -72x + 30x2 + -21x2 = 27 + 72x + 21x2 + -27 + -72x + -21x2

Combine like terms: 82x + -72x = 10x
1 + 10x + 30x2 + -21x2 = 27 + 72x + 21x2 + -27 + -72x + -21x2

Combine like terms: 30x2 + -21x2 = 9x2
1 + 10x + 9x2 = 27 + 72x + 21x2 + -27 + -72x + -21x2

Reorder the terms:
1 + 10x + 9x2 = 27 + -27 + 72x + -72x + 21x2 + -21x2

Combine like terms: 27 + -27 = 0
1 + 10x + 9x2 = 0 + 72x + -72x + 21x2 + -21x2
1 + 10x + 9x2 = 72x + -72x + 21x2 + -21x2

Combine like terms: 72x + -72x = 0
1 + 10x + 9x2 = 0 + 21x2 + -21x2
1 + 10x + 9x2 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
1 + 10x + 9x2 = 0

Factor a trinomial.
(1 + x)(1 + 9x) = 0


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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(1 + 9x)' equal to zero and attempt to solve:

Simplifying
1 + 9x = 0

Solving
1 + 9x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 9x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9x = 0 + -1
9x = 0 + -1

Combine like terms: 0 + -1 = -1
9x = -1

Divide each side by '9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Solution
x = {-1, -0.1111111111}

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