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Simplifying 3x(2x + -7) + -2x(x + 3) = 0 Reorder the terms: 3x(-7 + 2x) + -2x(x + 3) = 0 (-7 * 3x + 2x * 3x) + -2x(x + 3) = 0 (-21x + 6x2) + -2x(x + 3) = 0 Reorder the terms: -21x + 6x2 + -2x(3 + x) = 0 -21x + 6x2 + (3 * -2x + x * -2x) = 0 -21x + 6x2 + (-6x + -2x2) = 0 Reorder the terms: -21x + -6x + 6x2 + -2x2 = 0 Combine like terms: -21x + -6x = -27x -27x + 6x2 + -2x2 = 0 Combine like terms: 6x2 + -2x2 = 4x2 -27x + 4x2 = 0 Solving -27x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-27 + 4x) = 0Subproblem 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 '(-27 + 4x)' equal to zero and attempt to solve: Simplifying -27 + 4x = 0 Solving -27 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + 4x = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 4x = 0 + 27 4x = 0 + 27 Combine like terms: 0 + 27 = 27 4x = 27 Divide each side by '4'. x = 6.75 Simplifying x = 6.75Solution
x = {0, 6.75}
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