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Simplifying 5(x + 6)(x + -1) + -1(2x2 + -5x + 3) = 0 Reorder the terms: 5(6 + x)(x + -1) + -1(2x2 + -5x + 3) = 0 Reorder the terms: 5(6 + x)(-1 + x) + -1(2x2 + -5x + 3) = 0 Multiply (6 + x) * (-1 + x) 5(6(-1 + x) + x(-1 + x)) + -1(2x2 + -5x + 3) = 0 5((-1 * 6 + x * 6) + x(-1 + x)) + -1(2x2 + -5x + 3) = 0 5((-6 + 6x) + x(-1 + x)) + -1(2x2 + -5x + 3) = 0 5(-6 + 6x + (-1 * x + x * x)) + -1(2x2 + -5x + 3) = 0 5(-6 + 6x + (-1x + x2)) + -1(2x2 + -5x + 3) = 0 Combine like terms: 6x + -1x = 5x 5(-6 + 5x + x2) + -1(2x2 + -5x + 3) = 0 (-6 * 5 + 5x * 5 + x2 * 5) + -1(2x2 + -5x + 3) = 0 (-30 + 25x + 5x2) + -1(2x2 + -5x + 3) = 0 Reorder the terms: -30 + 25x + 5x2 + -1(3 + -5x + 2x2) = 0 -30 + 25x + 5x2 + (3 * -1 + -5x * -1 + 2x2 * -1) = 0 -30 + 25x + 5x2 + (-3 + 5x + -2x2) = 0 Reorder the terms: -30 + -3 + 25x + 5x + 5x2 + -2x2 = 0 Combine like terms: -30 + -3 = -33 -33 + 25x + 5x + 5x2 + -2x2 = 0 Combine like terms: 25x + 5x = 30x -33 + 30x + 5x2 + -2x2 = 0 Combine like terms: 5x2 + -2x2 = 3x2 -33 + 30x + 3x2 = 0 Solving -33 + 30x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + 10x + x2) = 0 Factor a trinomial. 3((-11 + -1x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve: Simplifying -11 + -1x = 0 Solving -11 + -1x = 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 + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x = 0 + 11 -1x = 0 + 11 Combine like terms: 0 + 11 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11Subproblem 2
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 = 1Solution
x = {-11, 1}
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