x^2-25=2(x-5)(x+3)

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Solution for x^2-25=2(x-5)(x+3) equation: 


Simplifying
x2 + -25 = 2(x + -5)(x + 3)

Reorder the terms:
-25 + x2 = 2(x + -5)(x + 3)

Reorder the terms:
-25 + x2 = 2(-5 + x)(x + 3)

Reorder the terms:
-25 + x2 = 2(-5 + x)(3 + x)

Multiply (-5 + x) * (3 + x)
-25 + x2 = 2(-5(3 + x) + x(3 + x))
-25 + x2 = 2((3 * -5 + x * -5) + x(3 + x))
-25 + x2 = 2((-15 + -5x) + x(3 + x))
-25 + x2 = 2(-15 + -5x + (3 * x + x * x))
-25 + x2 = 2(-15 + -5x + (3x + x2))

Combine like terms: -5x + 3x = -2x
-25 + x2 = 2(-15 + -2x + x2)
-25 + x2 = (-15 * 2 + -2x * 2 + x2 * 2)
-25 + x2 = (-30 + -4x + 2x2)

Solving
-25 + x2 = -30 + -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
-25 + 30 + 4x + x2 + -2x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2

Combine like terms: -25 + 30 = 5
5 + 4x + x2 + -2x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2

Combine like terms: x2 + -2x2 = -1x2
5 + 4x + -1x2 = -30 + -4x + 2x2 + 30 + 4x + -2x2

Reorder the terms:
5 + 4x + -1x2 = -30 + 30 + -4x + 4x + 2x2 + -2x2

Combine like terms: -30 + 30 = 0
5 + 4x + -1x2 = 0 + -4x + 4x + 2x2 + -2x2
5 + 4x + -1x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
5 + 4x + -1x2 = 0 + 2x2 + -2x2
5 + 4x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + 4x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(1 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {5, -1}

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