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Simplifying f(0) = 5(x + -1)(2x + 3) Reorder the terms for easier multiplication: 0f = 5(x + -1)(2x + 3) Anything times zero is zero. 0f = 5(x + -1)(2x + 3) Reorder the terms: 0 = 5(-1 + x)(2x + 3) Reorder the terms: 0 = 5(-1 + x)(3 + 2x) Multiply (-1 + x) * (3 + 2x) 0 = 5(-1(3 + 2x) + x(3 + 2x)) 0 = 5((3 * -1 + 2x * -1) + x(3 + 2x)) 0 = 5((-3 + -2x) + x(3 + 2x)) 0 = 5(-3 + -2x + (3 * x + 2x * x)) 0 = 5(-3 + -2x + (3x + 2x2)) Combine like terms: -2x + 3x = 1x 0 = 5(-3 + 1x + 2x2) 0 = (-3 * 5 + 1x * 5 + 2x2 * 5) 0 = (-15 + 5x + 10x2) Solving 0 = -15 + 5x + 10x2 Solving for variable 'x'. Combine like terms: 0 + 15 = 15 15 + -5x + -10x2 = -15 + 5x + 10x2 + 15 + -5x + -10x2 Reorder the terms: 15 + -5x + -10x2 = -15 + 15 + 5x + -5x + 10x2 + -10x2 Combine like terms: -15 + 15 = 0 15 + -5x + -10x2 = 0 + 5x + -5x + 10x2 + -10x2 15 + -5x + -10x2 = 5x + -5x + 10x2 + -10x2 Combine like terms: 5x + -5x = 0 15 + -5x + -10x2 = 0 + 10x2 + -10x2 15 + -5x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 15 + -5x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -1x + -2x2) = 0 Factor a trinomial. 5((1 + -1x)(3 + 2x)) = 0 Ignore the factor 5.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 '(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 = {1, -1.5}
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