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Simplifying (9x + 3 + 8x) + (5x + 3) = 6x(-4x + 8) Reorder the terms: (3 + 9x + 8x) + (5x + 3) = 6x(-4x + 8) Combine like terms: 9x + 8x = 17x (3 + 17x) + (5x + 3) = 6x(-4x + 8) Remove parenthesis around (3 + 17x) 3 + 17x + (5x + 3) = 6x(-4x + 8) Reorder the terms: 3 + 17x + (3 + 5x) = 6x(-4x + 8) Remove parenthesis around (3 + 5x) 3 + 17x + 3 + 5x = 6x(-4x + 8) Reorder the terms: 3 + 3 + 17x + 5x = 6x(-4x + 8) Combine like terms: 3 + 3 = 6 6 + 17x + 5x = 6x(-4x + 8) Combine like terms: 17x + 5x = 22x 6 + 22x = 6x(-4x + 8) Reorder the terms: 6 + 22x = 6x(8 + -4x) 6 + 22x = (8 * 6x + -4x * 6x) 6 + 22x = (48x + -24x2) Solving 6 + 22x = 48x + -24x2 Solving for variable 'x'. Combine like terms: 22x + -48x = -26x 6 + -26x + 24x2 = 48x + -24x2 + -48x + 24x2 Reorder the terms: 6 + -26x + 24x2 = 48x + -48x + -24x2 + 24x2 Combine like terms: 48x + -48x = 0 6 + -26x + 24x2 = 0 + -24x2 + 24x2 6 + -26x + 24x2 = -24x2 + 24x2 Combine like terms: -24x2 + 24x2 = 0 6 + -26x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -13x + 12x2) = 0 Factor a trinomial. 2((1 + -3x)(3 + -4x)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.3333333333Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {0.3333333333, 0.75}
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