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Simplifying 12(x2 + -6x + 5) + -6(x + -5)(x + -3) = 0 Reorder the terms: 12(5 + -6x + x2) + -6(x + -5)(x + -3) = 0 (5 * 12 + -6x * 12 + x2 * 12) + -6(x + -5)(x + -3) = 0 (60 + -72x + 12x2) + -6(x + -5)(x + -3) = 0 Reorder the terms: 60 + -72x + 12x2 + -6(-5 + x)(x + -3) = 0 Reorder the terms: 60 + -72x + 12x2 + -6(-5 + x)(-3 + x) = 0 Multiply (-5 + x) * (-3 + x) 60 + -72x + 12x2 + -6(-5(-3 + x) + x(-3 + x)) = 0 60 + -72x + 12x2 + -6((-3 * -5 + x * -5) + x(-3 + x)) = 0 60 + -72x + 12x2 + -6((15 + -5x) + x(-3 + x)) = 0 60 + -72x + 12x2 + -6(15 + -5x + (-3 * x + x * x)) = 0 60 + -72x + 12x2 + -6(15 + -5x + (-3x + x2)) = 0 Combine like terms: -5x + -3x = -8x 60 + -72x + 12x2 + -6(15 + -8x + x2) = 0 60 + -72x + 12x2 + (15 * -6 + -8x * -6 + x2 * -6) = 0 60 + -72x + 12x2 + (-90 + 48x + -6x2) = 0 Reorder the terms: 60 + -90 + -72x + 48x + 12x2 + -6x2 = 0 Combine like terms: 60 + -90 = -30 -30 + -72x + 48x + 12x2 + -6x2 = 0 Combine like terms: -72x + 48x = -24x -30 + -24x + 12x2 + -6x2 = 0 Combine like terms: 12x2 + -6x2 = 6x2 -30 + -24x + 6x2 = 0 Solving -30 + -24x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-5 + -4x + x2) = 0 Factor a trinomial. 6((-1 + -1x)(5 + -1x)) = 0 Ignore the factor 6.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 '(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 = {-1, 5}
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