x*x=(x+x+5)(x-6)

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Solution for x*x=(x+x+5)(x-6) equation: 


Simplifying
x * x = (x + x + 5)(x + -6)

Multiply x * x
x2 = (x + x + 5)(x + -6)

Reorder the terms:
x2 = (5 + x + x)(x + -6)

Combine like terms: x + x = 2x
x2 = (5 + 2x)(x + -6)

Reorder the terms:
x2 = (5 + 2x)(-6 + x)

Multiply (5 + 2x) * (-6 + x)
x2 = (5(-6 + x) + 2x * (-6 + x))
x2 = ((-6 * 5 + x * 5) + 2x * (-6 + x))
x2 = ((-30 + 5x) + 2x * (-6 + x))
x2 = (-30 + 5x + (-6 * 2x + x * 2x))
x2 = (-30 + 5x + (-12x + 2x2))

Combine like terms: 5x + -12x = -7x
x2 = (-30 + -7x + 2x2)

Solving
x2 = -30 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
30 + 7x + x2 + -2x2 = -30 + -7x + 2x2 + 30 + 7x + -2x2

Combine like terms: x2 + -2x2 = -1x2
30 + 7x + -1x2 = -30 + -7x + 2x2 + 30 + 7x + -2x2

Reorder the terms:
30 + 7x + -1x2 = -30 + 30 + -7x + 7x + 2x2 + -2x2

Combine like terms: -30 + 30 = 0
30 + 7x + -1x2 = 0 + -7x + 7x + 2x2 + -2x2
30 + 7x + -1x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
30 + 7x + -1x2 = 0 + 2x2 + -2x2
30 + 7x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
30 + 7x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(3 + x) = 0


Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {10, -3}

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