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Simplifying 0 = (6x + 3)(-5x + 11) Reorder the terms: 0 = (3 + 6x)(-5x + 11) Reorder the terms: 0 = (3 + 6x)(11 + -5x) Multiply (3 + 6x) * (11 + -5x) 0 = (3(11 + -5x) + 6x * (11 + -5x)) 0 = ((11 * 3 + -5x * 3) + 6x * (11 + -5x)) 0 = ((33 + -15x) + 6x * (11 + -5x)) 0 = (33 + -15x + (11 * 6x + -5x * 6x)) 0 = (33 + -15x + (66x + -30x2)) Combine like terms: -15x + 66x = 51x 0 = (33 + 51x + -30x2) Solving 0 = 33 + 51x + -30x2 Solving for variable 'x'. Combine like terms: 0 + -33 = -33 -33 + -51x + 30x2 = 33 + 51x + -30x2 + -33 + -51x + 30x2 Reorder the terms: -33 + -51x + 30x2 = 33 + -33 + 51x + -51x + -30x2 + 30x2 Combine like terms: 33 + -33 = 0 -33 + -51x + 30x2 = 0 + 51x + -51x + -30x2 + 30x2 -33 + -51x + 30x2 = 51x + -51x + -30x2 + 30x2 Combine like terms: 51x + -51x = 0 -33 + -51x + 30x2 = 0 + -30x2 + 30x2 -33 + -51x + 30x2 = -30x2 + 30x2 Combine like terms: -30x2 + 30x2 = 0 -33 + -51x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + -17x + 10x2) = 0 Factor a trinomial. 3((-1 + -2x)(11 + -5x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(11 + -5x)' equal to zero and attempt to solve: Simplifying 11 + -5x = 0 Solving 11 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -5x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -5x = 0 + -11 -5x = 0 + -11 Combine like terms: 0 + -11 = -11 -5x = -11 Divide each side by '-5'. x = 2.2 Simplifying x = 2.2Solution
x = {-0.5, 2.2}
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