2x(x+5)=(x-7)(x+5)

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Solution for 2x(x+5)=(x-7)(x+5) equation: 


Simplifying
2x(x + 5) = (x + -7)(x + 5)

Reorder the terms:
2x(5 + x) = (x + -7)(x + 5)
(5 * 2x + x * 2x) = (x + -7)(x + 5)
(10x + 2x2) = (x + -7)(x + 5)

Reorder the terms:
10x + 2x2 = (-7 + x)(x + 5)

Reorder the terms:
10x + 2x2 = (-7 + x)(5 + x)

Multiply (-7 + x) * (5 + x)
10x + 2x2 = (-7(5 + x) + x(5 + x))
10x + 2x2 = ((5 * -7 + x * -7) + x(5 + x))
10x + 2x2 = ((-35 + -7x) + x(5 + x))
10x + 2x2 = (-35 + -7x + (5 * x + x * x))
10x + 2x2 = (-35 + -7x + (5x + x2))

Combine like terms: -7x + 5x = -2x
10x + 2x2 = (-35 + -2x + x2)

Solving
10x + 2x2 = -35 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
35 + 10x + 2x + 2x2 + -1x2 = -35 + -2x + x2 + 35 + 2x + -1x2

Combine like terms: 10x + 2x = 12x
35 + 12x + 2x2 + -1x2 = -35 + -2x + x2 + 35 + 2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
35 + 12x + 1x2 = -35 + -2x + x2 + 35 + 2x + -1x2

Reorder the terms:
35 + 12x + 1x2 = -35 + 35 + -2x + 2x + x2 + -1x2

Combine like terms: -35 + 35 = 0
35 + 12x + 1x2 = 0 + -2x + 2x + x2 + -1x2
35 + 12x + 1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
35 + 12x + 1x2 = 0 + x2 + -1x2
35 + 12x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
35 + 12x + 1x2 = 0

Factor a trinomial.
(7 + x)(5 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-7, -5}

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