x[5+3x-(5x-6)]-5=0

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Solution for x[5+3x-(5x-6)]-5=0 equation: 


Simplifying
x[5 + 3x + -1(5x + -6)] + -5 = 0

Reorder the terms:
x[5 + 3x + -1(-6 + 5x)] + -5 = 0
x[5 + 3x + (-6 * -1 + 5x * -1)] + -5 = 0
x[5 + 3x + (6 + -5x)] + -5 = 0

Reorder the terms:
x[5 + 6 + 3x + -5x] + -5 = 0

Combine like terms: 5 + 6 = 11
x[11 + 3x + -5x] + -5 = 0

Combine like terms: 3x + -5x = -2x
x[11 + -2x] + -5 = 0
[11 * x + -2x * x] + -5 = 0
[11x + -2x2] + -5 = 0

Reorder the terms:
-5 + 11x + -2x2 = 0

Solving
-5 + 11x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + x)(1 + -2x) = 0


Subproblem 1
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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {5, 0.5}

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