15x^2=20-5x

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Solution for 15x^2=20-5x equation:


Simplifying
15x2 = 20 + -5x

Solving
15x2 = 20 + -5x

Solving for variable 'x'.

Reorder the terms:
-20 + 5x + 15x2 = 20 + -5x + -20 + 5x

Reorder the terms:
-20 + 5x + 15x2 = 20 + -20 + -5x + 5x

Combine like terms: 20 + -20 = 0
-20 + 5x + 15x2 = 0 + -5x + 5x
-20 + 5x + 15x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-20 + 5x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + x + 3x2) = 0

Factor a trinomial.
5((-4 + -3x)(1 + -1x)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333

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 = {-1.333333333, 1}

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