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Simplifying (x + 2)(2x + -3) + 6 + -4x = 0 Reorder the terms: (2 + x)(2x + -3) + 6 + -4x = 0 Reorder the terms: (2 + x)(-3 + 2x) + 6 + -4x = 0 Multiply (2 + x) * (-3 + 2x) (2(-3 + 2x) + x(-3 + 2x)) + 6 + -4x = 0 ((-3 * 2 + 2x * 2) + x(-3 + 2x)) + 6 + -4x = 0 ((-6 + 4x) + x(-3 + 2x)) + 6 + -4x = 0 (-6 + 4x + (-3 * x + 2x * x)) + 6 + -4x = 0 (-6 + 4x + (-3x + 2x2)) + 6 + -4x = 0 Combine like terms: 4x + -3x = 1x (-6 + 1x + 2x2) + 6 + -4x = 0 Reorder the terms: -6 + 6 + 1x + -4x + 2x2 = 0 Combine like terms: -6 + 6 = 0 0 + 1x + -4x + 2x2 = 0 1x + -4x + 2x2 = 0 Combine like terms: 1x + -4x = -3x -3x + 2x2 = 0 Solving -3x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + 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 '(-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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