x(2x+14)=(x+7)(x+4)

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Solution for x(2x+14)=(x+7)(x+4) equation: 


Simplifying
x(2x + 14) = (x + 7)(x + 4)

Reorder the terms:
x(14 + 2x) = (x + 7)(x + 4)
(14 * x + 2x * x) = (x + 7)(x + 4)
(14x + 2x2) = (x + 7)(x + 4)

Reorder the terms:
14x + 2x2 = (7 + x)(x + 4)

Reorder the terms:
14x + 2x2 = (7 + x)(4 + x)

Multiply (7 + x) * (4 + x)
14x + 2x2 = (7(4 + x) + x(4 + x))
14x + 2x2 = ((4 * 7 + x * 7) + x(4 + x))
14x + 2x2 = ((28 + 7x) + x(4 + x))
14x + 2x2 = (28 + 7x + (4 * x + x * x))
14x + 2x2 = (28 + 7x + (4x + x2))

Combine like terms: 7x + 4x = 11x
14x + 2x2 = (28 + 11x + x2)

Solving
14x + 2x2 = 28 + 11x + x2

Solving for variable 'x'.

Reorder the terms:
-28 + 14x + -11x + 2x2 + -1x2 = 28 + 11x + x2 + -28 + -11x + -1x2

Combine like terms: 14x + -11x = 3x
-28 + 3x + 2x2 + -1x2 = 28 + 11x + x2 + -28 + -11x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-28 + 3x + 1x2 = 28 + 11x + x2 + -28 + -11x + -1x2

Reorder the terms:
-28 + 3x + 1x2 = 28 + -28 + 11x + -11x + x2 + -1x2

Combine like terms: 28 + -28 = 0
-28 + 3x + 1x2 = 0 + 11x + -11x + x2 + -1x2
-28 + 3x + 1x2 = 11x + -11x + x2 + -1x2

Combine like terms: 11x + -11x = 0
-28 + 3x + 1x2 = 0 + x2 + -1x2
-28 + 3x + 1x2 = x2 + -1x2

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

Factor a trinomial.
(-7 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-7, 4}

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