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Simplifying 3.5x(2x + 3) + -3x(x + 1.5) = 0 Reorder the terms: 3.5x(3 + 2x) + -3x(x + 1.5) = 0 (3 * 3.5x + 2x * 3.5x) + -3x(x + 1.5) = 0 (10.5x + 7x2) + -3x(x + 1.5) = 0 Reorder the terms: 10.5x + 7x2 + -3x(1.5 + x) = 0 10.5x + 7x2 + (1.5 * -3x + x * -3x) = 0 10.5x + 7x2 + (-4.5x + -3x2) = 0 Reorder the terms: 10.5x + -4.5x + 7x2 + -3x2 = 0 Combine like terms: 10.5x + -4.5x = 6x 6x + 7x2 + -3x2 = 0 Combine like terms: 7x2 + -3x2 = 4x2 6x + 4x2 = 0 Solving 6x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + 2x) = 0 Ignore the factor 2.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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