x(x+1(x+2(x+3)))=10

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Solution for x(x+1(x+2(x+3)))=10 equation:


Simplifying
x(x + 1(x + 2(x + 3))) = 10

Reorder the terms:
x(x + 1(x + 2(3 + x))) = 10
x(x + 1(x + (3 * 2 + x * 2))) = 10
x(x + 1(x + (6 + 2x))) = 10

Reorder the terms:
x(x + 1(6 + x + 2x)) = 10

Combine like terms: x + 2x = 3x
x(x + 1(6 + 3x)) = 10
x(x + (6 * 1 + 3x * 1)) = 10
x(x + (6 + 3x)) = 10

Reorder the terms:
x(6 + x + 3x) = 10

Combine like terms: x + 3x = 4x
x(6 + 4x) = 10
(6 * x + 4x * x) = 10
(6x + 4x2) = 10

Solving
6x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 6x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 6x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 3x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {-2.5, 1}

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