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

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


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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

Factor a trinomial.
(6 + -1x)(7 + x) = 0

Subproblem 1

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Subproblem 2

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Solution

x = {6, -7}

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