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Simplifying 3x(x + -2) + -1(x + -6) = 23(x + -3) Reorder the terms: 3x(-2 + x) + -1(x + -6) = 23(x + -3) (-2 * 3x + x * 3x) + -1(x + -6) = 23(x + -3) (-6x + 3x2) + -1(x + -6) = 23(x + -3) Reorder the terms: -6x + 3x2 + -1(-6 + x) = 23(x + -3) -6x + 3x2 + (-6 * -1 + x * -1) = 23(x + -3) -6x + 3x2 + (6 + -1x) = 23(x + -3) Reorder the terms: 6 + -6x + -1x + 3x2 = 23(x + -3) Combine like terms: -6x + -1x = -7x 6 + -7x + 3x2 = 23(x + -3) Reorder the terms: 6 + -7x + 3x2 = 23(-3 + x) 6 + -7x + 3x2 = (-3 * 23 + x * 23) 6 + -7x + 3x2 = (-69 + 23x) Solving 6 + -7x + 3x2 = -69 + 23x Solving for variable 'x'. Reorder the terms: 6 + 69 + -7x + -23x + 3x2 = -69 + 23x + 69 + -23x Combine like terms: 6 + 69 = 75 75 + -7x + -23x + 3x2 = -69 + 23x + 69 + -23x Combine like terms: -7x + -23x = -30x 75 + -30x + 3x2 = -69 + 23x + 69 + -23x Reorder the terms: 75 + -30x + 3x2 = -69 + 69 + 23x + -23x Combine like terms: -69 + 69 = 0 75 + -30x + 3x2 = 0 + 23x + -23x 75 + -30x + 3x2 = 23x + -23x Combine like terms: 23x + -23x = 0 75 + -30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -10x + x2) = 0 Factor a trinomial. 3((5 + -1x)(5 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {5, 5}
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