6x^2=15-x

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Solution for 6x^2=15-x equation:


Simplifying
6x2 = 15 + -1x

Solving
6x2 = 15 + -1x

Solving for variable 'x'.

Reorder the terms:
-15 + x + 6x2 = 15 + -1x + -15 + x

Reorder the terms:
-15 + x + 6x2 = 15 + -15 + -1x + x

Combine like terms: 15 + -15 = 0
-15 + x + 6x2 = 0 + -1x + x
-15 + x + 6x2 = -1x + x

Combine like terms: -1x + x = 0
-15 + x + 6x2 = 0

Factor a trinomial.
(-5 + -3x)(3 + -2x) = 0

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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {-1.666666667, 1.5}

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