x(x+7)+198=(2x+14)(x-3)

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Solution for x(x+7)+198=(2x+14)(x-3) equation: 


Simplifying
x(x + 7) + 198 = (2x + 14)(x + -3)

Reorder the terms:
x(7 + x) + 198 = (2x + 14)(x + -3)
(7 * x + x * x) + 198 = (2x + 14)(x + -3)
(7x + x2) + 198 = (2x + 14)(x + -3)

Reorder the terms:
198 + 7x + x2 = (2x + 14)(x + -3)

Reorder the terms:
198 + 7x + x2 = (14 + 2x)(x + -3)

Reorder the terms:
198 + 7x + x2 = (14 + 2x)(-3 + x)

Multiply (14 + 2x) * (-3 + x)
198 + 7x + x2 = (14(-3 + x) + 2x * (-3 + x))
198 + 7x + x2 = ((-3 * 14 + x * 14) + 2x * (-3 + x))
198 + 7x + x2 = ((-42 + 14x) + 2x * (-3 + x))
198 + 7x + x2 = (-42 + 14x + (-3 * 2x + x * 2x))
198 + 7x + x2 = (-42 + 14x + (-6x + 2x2))

Combine like terms: 14x + -6x = 8x
198 + 7x + x2 = (-42 + 8x + 2x2)

Solving
198 + 7x + x2 = -42 + 8x + 2x2

Solving for variable 'x'.

Reorder the terms:
198 + 42 + 7x + -8x + x2 + -2x2 = -42 + 8x + 2x2 + 42 + -8x + -2x2

Combine like terms: 198 + 42 = 240
240 + 7x + -8x + x2 + -2x2 = -42 + 8x + 2x2 + 42 + -8x + -2x2

Combine like terms: 7x + -8x = -1x
240 + -1x + x2 + -2x2 = -42 + 8x + 2x2 + 42 + -8x + -2x2

Combine like terms: x2 + -2x2 = -1x2
240 + -1x + -1x2 = -42 + 8x + 2x2 + 42 + -8x + -2x2

Reorder the terms:
240 + -1x + -1x2 = -42 + 42 + 8x + -8x + 2x2 + -2x2

Combine like terms: -42 + 42 = 0
240 + -1x + -1x2 = 0 + 8x + -8x + 2x2 + -2x2
240 + -1x + -1x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
240 + -1x + -1x2 = 0 + 2x2 + -2x2
240 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
240 + -1x + -1x2 = 0

Factor a trinomial.
(15 + -1x)(16 + x) = 0


Subproblem 1
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15

Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {15, -16}

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