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Simplifying (x + -4)(x + 3) + (x + -9)(x + 3) = 0 Reorder the terms: (-4 + x)(x + 3) + (x + -9)(x + 3) = 0 Reorder the terms: (-4 + x)(3 + x) + (x + -9)(x + 3) = 0 Multiply (-4 + x) * (3 + x) (-4(3 + x) + x(3 + x)) + (x + -9)(x + 3) = 0 ((3 * -4 + x * -4) + x(3 + x)) + (x + -9)(x + 3) = 0 ((-12 + -4x) + x(3 + x)) + (x + -9)(x + 3) = 0 (-12 + -4x + (3 * x + x * x)) + (x + -9)(x + 3) = 0 (-12 + -4x + (3x + x2)) + (x + -9)(x + 3) = 0 Combine like terms: -4x + 3x = -1x (-12 + -1x + x2) + (x + -9)(x + 3) = 0 Reorder the terms: -12 + -1x + x2 + (-9 + x)(x + 3) = 0 Reorder the terms: -12 + -1x + x2 + (-9 + x)(3 + x) = 0 Multiply (-9 + x) * (3 + x) -12 + -1x + x2 + (-9(3 + x) + x(3 + x)) = 0 -12 + -1x + x2 + ((3 * -9 + x * -9) + x(3 + x)) = 0 -12 + -1x + x2 + ((-27 + -9x) + x(3 + x)) = 0 -12 + -1x + x2 + (-27 + -9x + (3 * x + x * x)) = 0 -12 + -1x + x2 + (-27 + -9x + (3x + x2)) = 0 Combine like terms: -9x + 3x = -6x -12 + -1x + x2 + (-27 + -6x + x2) = 0 Reorder the terms: -12 + -27 + -1x + -6x + x2 + x2 = 0 Combine like terms: -12 + -27 = -39 -39 + -1x + -6x + x2 + x2 = 0 Combine like terms: -1x + -6x = -7x -39 + -7x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 -39 + -7x + 2x2 = 0 Solving -39 + -7x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -1x)(13 + -2x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(13 + -2x)' equal to zero and attempt to solve: Simplifying 13 + -2x = 0 Solving 13 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2x = 0 + -13 -2x = 0 + -13 Combine like terms: 0 + -13 = -13 -2x = -13 Divide each side by '-2'. x = 6.5 Simplifying x = 6.5Solution
x = {-3, 6.5}
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