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Simplifying 0 = (3x + -2)(x + -5) Reorder the terms: 0 = (-2 + 3x)(x + -5) Reorder the terms: 0 = (-2 + 3x)(-5 + x) Multiply (-2 + 3x) * (-5 + x) 0 = (-2(-5 + x) + 3x * (-5 + x)) 0 = ((-5 * -2 + x * -2) + 3x * (-5 + x)) 0 = ((10 + -2x) + 3x * (-5 + x)) 0 = (10 + -2x + (-5 * 3x + x * 3x)) 0 = (10 + -2x + (-15x + 3x2)) Combine like terms: -2x + -15x = -17x 0 = (10 + -17x + 3x2) Solving 0 = 10 + -17x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + 17x + -3x2 = 10 + -17x + 3x2 + -10 + 17x + -3x2 Reorder the terms: -10 + 17x + -3x2 = 10 + -10 + -17x + 17x + 3x2 + -3x2 Combine like terms: 10 + -10 = 0 -10 + 17x + -3x2 = 0 + -17x + 17x + 3x2 + -3x2 -10 + 17x + -3x2 = -17x + 17x + 3x2 + -3x2 Combine like terms: -17x + 17x = 0 -10 + 17x + -3x2 = 0 + 3x2 + -3x2 -10 + 17x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -10 + 17x + -3x2 = 0 Factor a trinomial. (-5 + x)(2 + -3x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {5, 0.6666666667}
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