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Simplifying (9x + -3)(4 + -1x) = (9x + -3)(-3 + 2) Reorder the terms: (-3 + 9x)(4 + -1x) = (9x + -3)(-3 + 2) Multiply (-3 + 9x) * (4 + -1x) (-3(4 + -1x) + 9x * (4 + -1x)) = (9x + -3)(-3 + 2) ((4 * -3 + -1x * -3) + 9x * (4 + -1x)) = (9x + -3)(-3 + 2) ((-12 + 3x) + 9x * (4 + -1x)) = (9x + -3)(-3 + 2) (-12 + 3x + (4 * 9x + -1x * 9x)) = (9x + -3)(-3 + 2) (-12 + 3x + (36x + -9x2)) = (9x + -3)(-3 + 2) Combine like terms: 3x + 36x = 39x (-12 + 39x + -9x2) = (9x + -3)(-3 + 2) Reorder the terms: -12 + 39x + -9x2 = (-3 + 9x)(-3 + 2) Combine like terms: -3 + 2 = -1 -12 + 39x + -9x2 = (-3 + 9x)(-1) Reorder the terms for easier multiplication: -12 + 39x + -9x2 = -1(-3 + 9x) -12 + 39x + -9x2 = (-3 * -1 + 9x * -1) -12 + 39x + -9x2 = (3 + -9x) Solving -12 + 39x + -9x2 = 3 + -9x Solving for variable 'x'. Reorder the terms: -12 + -3 + 39x + 9x + -9x2 = 3 + -9x + -3 + 9x Combine like terms: -12 + -3 = -15 -15 + 39x + 9x + -9x2 = 3 + -9x + -3 + 9x Combine like terms: 39x + 9x = 48x -15 + 48x + -9x2 = 3 + -9x + -3 + 9x Reorder the terms: -15 + 48x + -9x2 = 3 + -3 + -9x + 9x Combine like terms: 3 + -3 = 0 -15 + 48x + -9x2 = 0 + -9x + 9x -15 + 48x + -9x2 = -9x + 9x Combine like terms: -9x + 9x = 0 -15 + 48x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 16x + -3x2) = 0 Factor a trinomial. 3((-5 + x)(1 + -3x)) = 0 Ignore the factor 3.Subproblem 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 '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {5, 0.3333333333}
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