0=18x^2-30x+12

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Solution for 0=18x^2-30x+12 equation:


Simplifying
0 = 18x2 + -30x + 12

Reorder the terms:
0 = 12 + -30x + 18x2

Solving
0 = 12 + -30x + 18x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + 30x + -18x2 = 12 + -30x + 18x2 + -12 + 30x + -18x2

Reorder the terms:
-12 + 30x + -18x2 = 12 + -12 + -30x + 30x + 18x2 + -18x2

Combine like terms: 12 + -12 = 0
-12 + 30x + -18x2 = 0 + -30x + 30x + 18x2 + -18x2
-12 + 30x + -18x2 = -30x + 30x + 18x2 + -18x2

Combine like terms: -30x + 30x = 0
-12 + 30x + -18x2 = 0 + 18x2 + -18x2
-12 + 30x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
-12 + 30x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 5x + -3x2) = 0

Factor a trinomial.
6((-1 + x)(2 + -3x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1

Subproblem 2

Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Solution

x = {1, 0.6666666667}

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