(4x^3+5x^2)(12x^2+10x)+(4x^3+5x^2)(12x^2+10x)=0

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Solution for (4x^3+5x^2)(12x^2+10x)+(4x^3+5x^2)(12x^2+10x)=0 equation:


Simplifying
(4x3 + 5x2)(12x2 + 10x) + (4x3 + 5x2)(12x2 + 10x) = 0

Reorder the terms:
(5x2 + 4x3)(12x2 + 10x) + (4x3 + 5x2)(12x2 + 10x) = 0

Reorder the terms:
(5x2 + 4x3)(10x + 12x2) + (4x3 + 5x2)(12x2 + 10x) = 0

Multiply (5x2 + 4x3) * (10x + 12x2)
(5x2 * (10x + 12x2) + 4x3 * (10x + 12x2)) + (4x3 + 5x2)(12x2 + 10x) = 0
((10x * 5x2 + 12x2 * 5x2) + 4x3 * (10x + 12x2)) + (4x3 + 5x2)(12x2 + 10x) = 0
((50x3 + 60x4) + 4x3 * (10x + 12x2)) + (4x3 + 5x2)(12x2 + 10x) = 0
(50x3 + 60x4 + (10x * 4x3 + 12x2 * 4x3)) + (4x3 + 5x2)(12x2 + 10x) = 0
(50x3 + 60x4 + (40x4 + 48x5)) + (4x3 + 5x2)(12x2 + 10x) = 0

Combine like terms: 60x4 + 40x4 = 100x4
(50x3 + 100x4 + 48x5) + (4x3 + 5x2)(12x2 + 10x) = 0

Reorder the terms:
50x3 + 100x4 + 48x5 + (5x2 + 4x3)(12x2 + 10x) = 0

Reorder the terms:
50x3 + 100x4 + 48x5 + (5x2 + 4x3)(10x + 12x2) = 0

Multiply (5x2 + 4x3) * (10x + 12x2)
50x3 + 100x4 + 48x5 + (5x2 * (10x + 12x2) + 4x3 * (10x + 12x2)) = 0
50x3 + 100x4 + 48x5 + ((10x * 5x2 + 12x2 * 5x2) + 4x3 * (10x + 12x2)) = 0
50x3 + 100x4 + 48x5 + ((50x3 + 60x4) + 4x3 * (10x + 12x2)) = 0
50x3 + 100x4 + 48x5 + (50x3 + 60x4 + (10x * 4x3 + 12x2 * 4x3)) = 0
50x3 + 100x4 + 48x5 + (50x3 + 60x4 + (40x4 + 48x5)) = 0

Combine like terms: 60x4 + 40x4 = 100x4
50x3 + 100x4 + 48x5 + (50x3 + 100x4 + 48x5) = 0

Reorder the terms:
50x3 + 50x3 + 100x4 + 100x4 + 48x5 + 48x5 = 0

Combine like terms: 50x3 + 50x3 = 100x3
100x3 + 100x4 + 100x4 + 48x5 + 48x5 = 0

Combine like terms: 100x4 + 100x4 = 200x4
100x3 + 200x4 + 48x5 + 48x5 = 0

Combine like terms: 48x5 + 48x5 = 96x5
100x3 + 200x4 + 96x5 = 0

Solving
100x3 + 200x4 + 96x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x3'.
4x3(25 + 50x + 24x2) = 0

Factor a trinomial.
4x3((5 + 4x)(5 + 6x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 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 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25

Subproblem 3

Set the factor '(5 + 6x)' equal to zero and attempt to solve: Simplifying 5 + 6x = 0 Solving 5 + 6x = 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 + 6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6x = 0 + -5 6x = 0 + -5 Combine like terms: 0 + -5 = -5 6x = -5 Divide each side by '6'. x = -0.8333333333 Simplifying x = -0.8333333333

Solution

x = {-1.25, -0.8333333333}

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