(x+3)(x+4)=(2x+6)(x-5)

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Solution for (x+3)(x+4)=(2x+6)(x-5) equation: 


Simplifying
(x + 3)(x + 4) = (2x + 6)(x + -5)

Reorder the terms:
(3 + x)(x + 4) = (2x + 6)(x + -5)

Reorder the terms:
(3 + x)(4 + x) = (2x + 6)(x + -5)

Multiply (3 + x) * (4 + x)
(3(4 + x) + x(4 + x)) = (2x + 6)(x + -5)
((4 * 3 + x * 3) + x(4 + x)) = (2x + 6)(x + -5)
((12 + 3x) + x(4 + x)) = (2x + 6)(x + -5)
(12 + 3x + (4 * x + x * x)) = (2x + 6)(x + -5)
(12 + 3x + (4x + x2)) = (2x + 6)(x + -5)

Combine like terms: 3x + 4x = 7x
(12 + 7x + x2) = (2x + 6)(x + -5)

Reorder the terms:
12 + 7x + x2 = (6 + 2x)(x + -5)

Reorder the terms:
12 + 7x + x2 = (6 + 2x)(-5 + x)

Multiply (6 + 2x) * (-5 + x)
12 + 7x + x2 = (6(-5 + x) + 2x * (-5 + x))
12 + 7x + x2 = ((-5 * 6 + x * 6) + 2x * (-5 + x))
12 + 7x + x2 = ((-30 + 6x) + 2x * (-5 + x))
12 + 7x + x2 = (-30 + 6x + (-5 * 2x + x * 2x))
12 + 7x + x2 = (-30 + 6x + (-10x + 2x2))

Combine like terms: 6x + -10x = -4x
12 + 7x + x2 = (-30 + -4x + 2x2)

Solving
12 + 7x + x2 = -30 + -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
12 + 30 + 7x + 4x + x2 + -2x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2

Combine like terms: 12 + 30 = 42
42 + 7x + 4x + x2 + -2x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2

Combine like terms: 7x + 4x = 11x
42 + 11x + x2 + -2x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2

Combine like terms: x2 + -2x2 = -1x2
42 + 11x + -1x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2

Reorder the terms:
42 + 11x + -1x2 = -30 + 30 + -4x + 4x + 2x2 + -2x2

Combine like terms: -30 + 30 = 0
42 + 11x + -1x2 = 0 + -4x + 4x + 2x2 + -2x2
42 + 11x + -1x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
42 + 11x + -1x2 = 0 + 2x2 + -2x2
42 + 11x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
42 + 11x + -1x2 = 0

Factor a trinomial.
(14 + -1x)(3 + x) = 0


Subproblem 1
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14

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 = {14, -3}

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