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Simplifying 3x(4x + -5) + -2x(5x + -4) = 0 Reorder the terms: 3x(-5 + 4x) + -2x(5x + -4) = 0 (-5 * 3x + 4x * 3x) + -2x(5x + -4) = 0 (-15x + 12x2) + -2x(5x + -4) = 0 Reorder the terms: -15x + 12x2 + -2x(-4 + 5x) = 0 -15x + 12x2 + (-4 * -2x + 5x * -2x) = 0 -15x + 12x2 + (8x + -10x2) = 0 Reorder the terms: -15x + 8x + 12x2 + -10x2 = 0 Combine like terms: -15x + 8x = -7x -7x + 12x2 + -10x2 = 0 Combine like terms: 12x2 + -10x2 = 2x2 -7x + 2x2 = 0 Solving -7x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + 2x) = 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 '(-7 + 2x)' equal to zero and attempt to solve: Simplifying -7 + 2x = 0 Solving -7 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2x = 0 + 7 2x = 0 + 7 Combine like terms: 0 + 7 = 7 2x = 7 Divide each side by '2'. x = 3.5 Simplifying x = 3.5Solution
x = {0, 3.5}
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