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Simplifying 6 = -16x2 + 24x + 6 Reorder the terms: 6 = 6 + 24x + -16x2 Add '-6' to each side of the equation. 6 + -6 = 6 + 24x + -6 + -16x2 Combine like terms: 6 + -6 = 0 0 = 6 + 24x + -6 + -16x2 Reorder the terms: 0 = 6 + -6 + 24x + -16x2 Combine like terms: 6 + -6 = 0 0 = 0 + 24x + -16x2 0 = 24x + -16x2 Solving 0 = 24x + -16x2 Solving for variable 'x'. Remove the zero: -24x + 16x2 = 24x + -16x2 + -24x + 16x2 Reorder the terms: -24x + 16x2 = 24x + -24x + -16x2 + 16x2 Combine like terms: 24x + -24x = 0 -24x + 16x2 = 0 + -16x2 + 16x2 -24x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -24x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8x'. 8x(-3 + 2x) = 0 Ignore the factor 8.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 '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Solution
x = {0, 1.5}
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