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Simplifying 30x3 = 21x2 + 135x Reorder the terms: 30x3 = 135x + 21x2 Solving 30x3 = 135x + 21x2 Solving for variable 'x'. Reorder the terms: -135x + -21x2 + 30x3 = 135x + 21x2 + -135x + -21x2 Reorder the terms: -135x + -21x2 + 30x3 = 135x + -135x + 21x2 + -21x2 Combine like terms: 135x + -135x = 0 -135x + -21x2 + 30x3 = 0 + 21x2 + -21x2 -135x + -21x2 + 30x3 = 21x2 + -21x2 Combine like terms: 21x2 + -21x2 = 0 -135x + -21x2 + 30x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-45 + -7x + 10x2) = 0 Factor a trinomial. 3x((-9 + -5x)(5 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-9 + -5x)' equal to zero and attempt to solve: Simplifying -9 + -5x = 0 Solving -9 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -5x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5x = 0 + 9 -5x = 0 + 9 Combine like terms: 0 + 9 = 9 -5x = 9 Divide each side by '-5'. x = -1.8 Simplifying x = -1.8Subproblem 3
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {0, -1.8, 2.5}
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