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Simplifying 6x2 + -15x + 5 = 12x + 5 Reorder the terms: 5 + -15x + 6x2 = 12x + 5 Reorder the terms: 5 + -15x + 6x2 = 5 + 12x Add '-5' to each side of the equation. 5 + -15x + -5 + 6x2 = 5 + -5 + 12x Reorder the terms: 5 + -5 + -15x + 6x2 = 5 + -5 + 12x Combine like terms: 5 + -5 = 0 0 + -15x + 6x2 = 5 + -5 + 12x -15x + 6x2 = 5 + -5 + 12x Combine like terms: 5 + -5 = 0 -15x + 6x2 = 0 + 12x -15x + 6x2 = 12x Solving -15x + 6x2 = 12x Solving for variable 'x'. Reorder the terms: -15x + -12x + 6x2 = 12x + -12x Combine like terms: -15x + -12x = -27x -27x + 6x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -27x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-9 + 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 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 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 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Divide each side by '2'. x = 4.5 Simplifying x = 4.5Solution
x = {0, 4.5}
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