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Simplifying 3x(6x + -5) = -3x(2x + 1) Reorder the terms: 3x(-5 + 6x) = -3x(2x + 1) (-5 * 3x + 6x * 3x) = -3x(2x + 1) (-15x + 18x2) = -3x(2x + 1) Reorder the terms: -15x + 18x2 = -3x(1 + 2x) -15x + 18x2 = (1 * -3x + 2x * -3x) -15x + 18x2 = (-3x + -6x2) Solving -15x + 18x2 = -3x + -6x2 Solving for variable 'x'. Reorder the terms: -15x + 3x + 18x2 + 6x2 = -3x + -6x2 + 3x + 6x2 Combine like terms: -15x + 3x = -12x -12x + 18x2 + 6x2 = -3x + -6x2 + 3x + 6x2 Combine like terms: 18x2 + 6x2 = 24x2 -12x + 24x2 = -3x + -6x2 + 3x + 6x2 Reorder the terms: -12x + 24x2 = -3x + 3x + -6x2 + 6x2 Combine like terms: -3x + 3x = 0 -12x + 24x2 = 0 + -6x2 + 6x2 -12x + 24x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -12x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '12x'. 12x(-1 + 2x) = 0 Ignore the factor 12.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 '(-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 = 0.5Solution
x = {0, 0.5}
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