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Simplifying 3x(x + -5) + (x + -3)(x + -2) + 18 = 0 Reorder the terms: 3x(-5 + x) + (x + -3)(x + -2) + 18 = 0 (-5 * 3x + x * 3x) + (x + -3)(x + -2) + 18 = 0 (-15x + 3x2) + (x + -3)(x + -2) + 18 = 0 Reorder the terms: -15x + 3x2 + (-3 + x)(x + -2) + 18 = 0 Reorder the terms: -15x + 3x2 + (-3 + x)(-2 + x) + 18 = 0 Multiply (-3 + x) * (-2 + x) -15x + 3x2 + (-3(-2 + x) + x(-2 + x)) + 18 = 0 -15x + 3x2 + ((-2 * -3 + x * -3) + x(-2 + x)) + 18 = 0 -15x + 3x2 + ((6 + -3x) + x(-2 + x)) + 18 = 0 -15x + 3x2 + (6 + -3x + (-2 * x + x * x)) + 18 = 0 -15x + 3x2 + (6 + -3x + (-2x + x2)) + 18 = 0 Combine like terms: -3x + -2x = -5x -15x + 3x2 + (6 + -5x + x2) + 18 = 0 Reorder the terms: 6 + 18 + -15x + -5x + 3x2 + x2 = 0 Combine like terms: 6 + 18 = 24 24 + -15x + -5x + 3x2 + x2 = 0 Combine like terms: -15x + -5x = -20x 24 + -20x + 3x2 + x2 = 0 Combine like terms: 3x2 + x2 = 4x2 24 + -20x + 4x2 = 0 Solving 24 + -20x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -5x + x2) = 0 Factor a trinomial. 4((2 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {2, 3}
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