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Simplifying (3x + 3)(2x + -5) = 0 Reorder the terms: (3 + 3x)(2x + -5) = 0 Reorder the terms: (3 + 3x)(-5 + 2x) = 0 Multiply (3 + 3x) * (-5 + 2x) (3(-5 + 2x) + 3x * (-5 + 2x)) = 0 ((-5 * 3 + 2x * 3) + 3x * (-5 + 2x)) = 0 ((-15 + 6x) + 3x * (-5 + 2x)) = 0 (-15 + 6x + (-5 * 3x + 2x * 3x)) = 0 (-15 + 6x + (-15x + 6x2)) = 0 Combine like terms: 6x + -15x = -9x (-15 + -9x + 6x2) = 0 Solving -15 + -9x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -3x + 2x2) = 0 Factor a trinomial. 3((-1 + -1x)(5 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-1, 2.5}
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