x(x+1)=4[x+(x+1)]-14

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Solution for x(x+1)=4[x+(x+1)]-14 equation: 


Simplifying
x(x + 1) = 4[x + (x + 1)] + -14

Reorder the terms:
x(1 + x) = 4[x + (x + 1)] + -14
(1 * x + x * x) = 4[x + (x + 1)] + -14
(1x + x2) = 4[x + (x + 1)] + -14

Reorder the terms:
1x + x2 = 4[x + (1 + x)] + -14

Remove parenthesis around (1 + x)
1x + x2 = 4[x + 1 + x] + -14

Reorder the terms:
1x + x2 = 4[1 + x + x] + -14

Combine like terms: x + x = 2x
1x + x2 = 4[1 + 2x] + -14
1x + x2 = [1 * 4 + 2x * 4] + -14
1x + x2 = [4 + 8x] + -14

Reorder the terms:
1x + x2 = 4 + -14 + 8x

Combine like terms: 4 + -14 = -10
1x + x2 = -10 + 8x

Solving
1x + x2 = -10 + 8x

Solving for variable 'x'.

Reorder the terms:
10 + 1x + -8x + x2 = -10 + 8x + 10 + -8x

Combine like terms: 1x + -8x = -7x
10 + -7x + x2 = -10 + 8x + 10 + -8x

Reorder the terms:
10 + -7x + x2 = -10 + 10 + 8x + -8x

Combine like terms: -10 + 10 = 0
10 + -7x + x2 = 0 + 8x + -8x
10 + -7x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
10 + -7x + x2 = 0

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


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
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
Solution
x = {2, 5}

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