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Simplifying (2x + -3)(x + 4) = 21(x + -2) Reorder the terms: (-3 + 2x)(x + 4) = 21(x + -2) Reorder the terms: (-3 + 2x)(4 + x) = 21(x + -2) Multiply (-3 + 2x) * (4 + x) (-3(4 + x) + 2x * (4 + x)) = 21(x + -2) ((4 * -3 + x * -3) + 2x * (4 + x)) = 21(x + -2) ((-12 + -3x) + 2x * (4 + x)) = 21(x + -2) (-12 + -3x + (4 * 2x + x * 2x)) = 21(x + -2) (-12 + -3x + (8x + 2x2)) = 21(x + -2) Combine like terms: -3x + 8x = 5x (-12 + 5x + 2x2) = 21(x + -2) Reorder the terms: -12 + 5x + 2x2 = 21(-2 + x) -12 + 5x + 2x2 = (-2 * 21 + x * 21) -12 + 5x + 2x2 = (-42 + 21x) Solving -12 + 5x + 2x2 = -42 + 21x Solving for variable 'x'. Reorder the terms: -12 + 42 + 5x + -21x + 2x2 = -42 + 21x + 42 + -21x Combine like terms: -12 + 42 = 30 30 + 5x + -21x + 2x2 = -42 + 21x + 42 + -21x Combine like terms: 5x + -21x = -16x 30 + -16x + 2x2 = -42 + 21x + 42 + -21x Reorder the terms: 30 + -16x + 2x2 = -42 + 42 + 21x + -21x Combine like terms: -42 + 42 = 0 30 + -16x + 2x2 = 0 + 21x + -21x 30 + -16x + 2x2 = 21x + -21x Combine like terms: 21x + -21x = 0 30 + -16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -8x + x2) = 0 Factor a trinomial. 2((3 + -1x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 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 '(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 = {3, 5}
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