4x^2-20=-5x^2-6x-5

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Solution for 4x^2-20=-5x^2-6x-5 equation:


Simplifying
4x2 + -20 = -5x2 + -6x + -5

Reorder the terms:
-20 + 4x2 = -5x2 + -6x + -5

Reorder the terms:
-20 + 4x2 = -5 + -6x + -5x2

Solving
-20 + 4x2 = -5 + -6x + -5x2

Solving for variable 'x'.

Reorder the terms:
-20 + 5 + 6x + 4x2 + 5x2 = -5 + -6x + -5x2 + 5 + 6x + 5x2

Combine like terms: -20 + 5 = -15
-15 + 6x + 4x2 + 5x2 = -5 + -6x + -5x2 + 5 + 6x + 5x2

Combine like terms: 4x2 + 5x2 = 9x2
-15 + 6x + 9x2 = -5 + -6x + -5x2 + 5 + 6x + 5x2

Reorder the terms:
-15 + 6x + 9x2 = -5 + 5 + -6x + 6x + -5x2 + 5x2

Combine like terms: -5 + 5 = 0
-15 + 6x + 9x2 = 0 + -6x + 6x + -5x2 + 5x2
-15 + 6x + 9x2 = -6x + 6x + -5x2 + 5x2

Combine like terms: -6x + 6x = 0
-15 + 6x + 9x2 = 0 + -5x2 + 5x2
-15 + 6x + 9x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-15 + 6x + 9x2 = 0

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

Factor a trinomial.
3((-5 + -3x)(1 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-5 + -3x)' equal to zero and attempt to solve: Simplifying -5 + -3x = 0 Solving -5 + -3x = 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 + -3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x = 0 + 5 -3x = 0 + 5 Combine like terms: 0 + 5 = 5 -3x = 5 Divide each side by '-3'. x = -1.666666667 Simplifying x = -1.666666667

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 = {-1.666666667, 1}

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