90x^2=6-12x

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Solution for 90x^2=6-12x equation:


Simplifying
90x2 = 6 + -12x

Solving
90x2 = 6 + -12x

Solving for variable 'x'.

Reorder the terms:
-6 + 12x + 90x2 = 6 + -12x + -6 + 12x

Reorder the terms:
-6 + 12x + 90x2 = 6 + -6 + -12x + 12x

Combine like terms: 6 + -6 = 0
-6 + 12x + 90x2 = 0 + -12x + 12x
-6 + 12x + 90x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
-6 + 12x + 90x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 2x + 15x2) = 0

Factor a trinomial.
6((-1 + -3x)(1 + -5x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333

Subproblem 2

Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2

Solution

x = {-0.3333333333, 0.2}

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