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Simplifying (3x + 4)(x + -10) + (10 + -1x)(x + -8) = 0 Reorder the terms: (4 + 3x)(x + -10) + (10 + -1x)(x + -8) = 0 Reorder the terms: (4 + 3x)(-10 + x) + (10 + -1x)(x + -8) = 0 Multiply (4 + 3x) * (-10 + x) (4(-10 + x) + 3x * (-10 + x)) + (10 + -1x)(x + -8) = 0 ((-10 * 4 + x * 4) + 3x * (-10 + x)) + (10 + -1x)(x + -8) = 0 ((-40 + 4x) + 3x * (-10 + x)) + (10 + -1x)(x + -8) = 0 (-40 + 4x + (-10 * 3x + x * 3x)) + (10 + -1x)(x + -8) = 0 (-40 + 4x + (-30x + 3x2)) + (10 + -1x)(x + -8) = 0 Combine like terms: 4x + -30x = -26x (-40 + -26x + 3x2) + (10 + -1x)(x + -8) = 0 Reorder the terms: -40 + -26x + 3x2 + (10 + -1x)(-8 + x) = 0 Multiply (10 + -1x) * (-8 + x) -40 + -26x + 3x2 + (10(-8 + x) + -1x * (-8 + x)) = 0 -40 + -26x + 3x2 + ((-8 * 10 + x * 10) + -1x * (-8 + x)) = 0 -40 + -26x + 3x2 + ((-80 + 10x) + -1x * (-8 + x)) = 0 -40 + -26x + 3x2 + (-80 + 10x + (-8 * -1x + x * -1x)) = 0 -40 + -26x + 3x2 + (-80 + 10x + (8x + -1x2)) = 0 Combine like terms: 10x + 8x = 18x -40 + -26x + 3x2 + (-80 + 18x + -1x2) = 0 Reorder the terms: -40 + -80 + -26x + 18x + 3x2 + -1x2 = 0 Combine like terms: -40 + -80 = -120 -120 + -26x + 18x + 3x2 + -1x2 = 0 Combine like terms: -26x + 18x = -8x -120 + -8x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 -120 + -8x + 2x2 = 0 Solving -120 + -8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + -4x + x2) = 0 Factor a trinomial. 2((-6 + -1x)(10 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-6, 10}
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