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Simplifying 0 = 2(x + 3)(x + -7) Reorder the terms: 0 = 2(3 + x)(x + -7) Reorder the terms: 0 = 2(3 + x)(-7 + x) Multiply (3 + x) * (-7 + x) 0 = 2(3(-7 + x) + x(-7 + x)) 0 = 2((-7 * 3 + x * 3) + x(-7 + x)) 0 = 2((-21 + 3x) + x(-7 + x)) 0 = 2(-21 + 3x + (-7 * x + x * x)) 0 = 2(-21 + 3x + (-7x + x2)) Combine like terms: 3x + -7x = -4x 0 = 2(-21 + -4x + x2) 0 = (-21 * 2 + -4x * 2 + x2 * 2) 0 = (-42 + -8x + 2x2) Solving 0 = -42 + -8x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 42 = 42 42 + 8x + -2x2 = -42 + -8x + 2x2 + 42 + 8x + -2x2 Reorder the terms: 42 + 8x + -2x2 = -42 + 42 + -8x + 8x + 2x2 + -2x2 Combine like terms: -42 + 42 = 0 42 + 8x + -2x2 = 0 + -8x + 8x + 2x2 + -2x2 42 + 8x + -2x2 = -8x + 8x + 2x2 + -2x2 Combine like terms: -8x + 8x = 0 42 + 8x + -2x2 = 0 + 2x2 + -2x2 42 + 8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 42 + 8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 4x + -1x2) = 0 Factor a trinomial. 2((7 + -1x)(3 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {7, -3}
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