(x+(x+2)+(x+4))3=(x(x+2))-152

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Solution for (x+(x+2)+(x+4))3=(x(x+2))-152 equation:


Simplifying
(x + (x + 2) + (x + 4)) * 3 = (x(x + 2)) + -152

Reorder the terms:
(x + (2 + x) + (x + 4)) * 3 = (x(x + 2)) + -152

Remove parenthesis around (2 + x)
(x + 2 + x + (x + 4)) * 3 = (x(x + 2)) + -152

Reorder the terms:
(x + 2 + x + (4 + x)) * 3 = (x(x + 2)) + -152

Remove parenthesis around (4 + x)
(x + 2 + x + 4 + x) * 3 = (x(x + 2)) + -152

Reorder the terms:
(2 + 4 + x + x + x) * 3 = (x(x + 2)) + -152

Combine like terms: 2 + 4 = 6
(6 + x + x + x) * 3 = (x(x + 2)) + -152

Combine like terms: x + x = 2x
(6 + 2x + x) * 3 = (x(x + 2)) + -152

Combine like terms: 2x + x = 3x
(6 + 3x) * 3 = (x(x + 2)) + -152

Reorder the terms for easier multiplication:
3(6 + 3x) = (x(x + 2)) + -152
(6 * 3 + 3x * 3) = (x(x + 2)) + -152
(18 + 9x) = (x(x + 2)) + -152

Reorder the terms:
18 + 9x = (x(2 + x)) + -152
18 + 9x = ((2 * x + x * x)) + -152
18 + 9x = ((2x + x2)) + -152
18 + 9x = (2x + x2) + -152

Remove parenthesis around (2x + x2)
18 + 9x = 2x + x2 + -152

Reorder the terms:
18 + 9x = -152 + 2x + x2

Solving
18 + 9x = -152 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
18 + 152 + 9x + -2x + -1x2 = -152 + 2x + x2 + 152 + -2x + -1x2

Combine like terms: 18 + 152 = 170
170 + 9x + -2x + -1x2 = -152 + 2x + x2 + 152 + -2x + -1x2

Combine like terms: 9x + -2x = 7x
170 + 7x + -1x2 = -152 + 2x + x2 + 152 + -2x + -1x2

Reorder the terms:
170 + 7x + -1x2 = -152 + 152 + 2x + -2x + x2 + -1x2

Combine like terms: -152 + 152 = 0
170 + 7x + -1x2 = 0 + 2x + -2x + x2 + -1x2
170 + 7x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
170 + 7x + -1x2 = 0 + x2 + -1x2
170 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
170 + 7x + -1x2 = 0

Factor a trinomial.
(17 + -1x)(10 + x) = 0

Subproblem 1

Set the factor '(17 + -1x)' equal to zero and attempt to solve: Simplifying 17 + -1x = 0 Solving 17 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1x = 0 + -17 -1x = 0 + -17 Combine like terms: 0 + -17 = -17 -1x = -17 Divide each side by '-1'. x = 17 Simplifying x = 17

Subproblem 2

Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 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 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10

Solution

x = {17, -10}

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