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Simplifying (3x + 4)(3x + 4) = 7(3x + 4) Reorder the terms: (4 + 3x)(3x + 4) = 7(3x + 4) Reorder the terms: (4 + 3x)(4 + 3x) = 7(3x + 4) Multiply (4 + 3x) * (4 + 3x) (4(4 + 3x) + 3x * (4 + 3x)) = 7(3x + 4) ((4 * 4 + 3x * 4) + 3x * (4 + 3x)) = 7(3x + 4) ((16 + 12x) + 3x * (4 + 3x)) = 7(3x + 4) (16 + 12x + (4 * 3x + 3x * 3x)) = 7(3x + 4) (16 + 12x + (12x + 9x2)) = 7(3x + 4) Combine like terms: 12x + 12x = 24x (16 + 24x + 9x2) = 7(3x + 4) Reorder the terms: 16 + 24x + 9x2 = 7(4 + 3x) 16 + 24x + 9x2 = (4 * 7 + 3x * 7) 16 + 24x + 9x2 = (28 + 21x) Solving 16 + 24x + 9x2 = 28 + 21x Solving for variable 'x'. Reorder the terms: 16 + -28 + 24x + -21x + 9x2 = 28 + 21x + -28 + -21x Combine like terms: 16 + -28 = -12 -12 + 24x + -21x + 9x2 = 28 + 21x + -28 + -21x Combine like terms: 24x + -21x = 3x -12 + 3x + 9x2 = 28 + 21x + -28 + -21x Reorder the terms: -12 + 3x + 9x2 = 28 + -28 + 21x + -21x Combine like terms: 28 + -28 = 0 -12 + 3x + 9x2 = 0 + 21x + -21x -12 + 3x + 9x2 = 21x + -21x Combine like terms: 21x + -21x = 0 -12 + 3x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + x + 3x2) = 0 Factor a trinomial. 3((-4 + -3x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333Subproblem 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 = {-1.333333333, 1}
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