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Simplifying 9x2 + -45x + 35 = 6x2 + -30x + 23 Reorder the terms: 35 + -45x + 9x2 = 6x2 + -30x + 23 Reorder the terms: 35 + -45x + 9x2 = 23 + -30x + 6x2 Solving 35 + -45x + 9x2 = 23 + -30x + 6x2 Solving for variable 'x'. Reorder the terms: 35 + -23 + -45x + 30x + 9x2 + -6x2 = 23 + -30x + 6x2 + -23 + 30x + -6x2 Combine like terms: 35 + -23 = 12 12 + -45x + 30x + 9x2 + -6x2 = 23 + -30x + 6x2 + -23 + 30x + -6x2 Combine like terms: -45x + 30x = -15x 12 + -15x + 9x2 + -6x2 = 23 + -30x + 6x2 + -23 + 30x + -6x2 Combine like terms: 9x2 + -6x2 = 3x2 12 + -15x + 3x2 = 23 + -30x + 6x2 + -23 + 30x + -6x2 Reorder the terms: 12 + -15x + 3x2 = 23 + -23 + -30x + 30x + 6x2 + -6x2 Combine like terms: 23 + -23 = 0 12 + -15x + 3x2 = 0 + -30x + 30x + 6x2 + -6x2 12 + -15x + 3x2 = -30x + 30x + 6x2 + -6x2 Combine like terms: -30x + 30x = 0 12 + -15x + 3x2 = 0 + 6x2 + -6x2 12 + -15x + 3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 12 + -15x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -5x + x2) = 0 Factor a trinomial. 3((1 + -1x)(4 + -1x)) = 0 Ignore the factor 3.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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {1, 4}
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