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Simplifying (36x4 + 21x3 + -30x2) + -1(27x4 + -12x2) = 0 Reorder the terms: (-30x2 + 21x3 + 36x4) + -1(27x4 + -12x2) = 0 Remove parenthesis around (-30x2 + 21x3 + 36x4) -30x2 + 21x3 + 36x4 + -1(27x4 + -12x2) = 0 Reorder the terms: -30x2 + 21x3 + 36x4 + -1(-12x2 + 27x4) = 0 -30x2 + 21x3 + 36x4 + (-12x2 * -1 + 27x4 * -1) = 0 -30x2 + 21x3 + 36x4 + (12x2 + -27x4) = 0 Reorder the terms: -30x2 + 12x2 + 21x3 + 36x4 + -27x4 = 0 Combine like terms: -30x2 + 12x2 = -18x2 -18x2 + 21x3 + 36x4 + -27x4 = 0 Combine like terms: 36x4 + -27x4 = 9x4 -18x2 + 21x3 + 9x4 = 0 Solving -18x2 + 21x3 + 9x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(-6 + 7x + 3x2) = 0 Factor a trinomial. 3x2((-3 + -1x)(2 + -3x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 3
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 = 0.6666666667Solution
x = {0, -3, 0.6666666667}
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