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Simplifying 3(-3x(2x + 5) + 3(4x + -5)) = 18x + -90 Reorder the terms: 3(-3x(5 + 2x) + 3(4x + -5)) = 18x + -90 3((5 * -3x + 2x * -3x) + 3(4x + -5)) = 18x + -90 3((-15x + -6x2) + 3(4x + -5)) = 18x + -90 Reorder the terms: 3(-15x + -6x2 + 3(-5 + 4x)) = 18x + -90 3(-15x + -6x2 + (-5 * 3 + 4x * 3)) = 18x + -90 3(-15x + -6x2 + (-15 + 12x)) = 18x + -90 Reorder the terms: 3(-15 + -15x + 12x + -6x2) = 18x + -90 Combine like terms: -15x + 12x = -3x 3(-15 + -3x + -6x2) = 18x + -90 (-15 * 3 + -3x * 3 + -6x2 * 3) = 18x + -90 (-45 + -9x + -18x2) = 18x + -90 Reorder the terms: -45 + -9x + -18x2 = -90 + 18x Solving -45 + -9x + -18x2 = -90 + 18x Solving for variable 'x'. Reorder the terms: -45 + 90 + -9x + -18x + -18x2 = -90 + 18x + 90 + -18x Combine like terms: -45 + 90 = 45 45 + -9x + -18x + -18x2 = -90 + 18x + 90 + -18x Combine like terms: -9x + -18x = -27x 45 + -27x + -18x2 = -90 + 18x + 90 + -18x Reorder the terms: 45 + -27x + -18x2 = -90 + 90 + 18x + -18x Combine like terms: -90 + 90 = 0 45 + -27x + -18x2 = 0 + 18x + -18x 45 + -27x + -18x2 = 18x + -18x Combine like terms: 18x + -18x = 0 45 + -27x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(5 + -3x + -2x2) = 0 Factor a trinomial. 9((1 + -1x)(5 + 2x)) = 0 Ignore the factor 9.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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