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Simplifying 6x4 + -45x3 = 24x2 Reorder the terms: -45x3 + 6x4 = 24x2 Solving -45x3 + 6x4 = 24x2 Solving for variable 'x'. Reorder the terms: -24x2 + -45x3 + 6x4 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -24x2 + -45x3 + 6x4 = 0 Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(-8 + -15x + 2x2) = 0 Factor a trinomial. 3x2((-1 + -2x)(8 + -1x)) = 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 '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 3
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {0, -0.5, 8}
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