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Simplifying 0 = (9x + 7)(6x + 4) Reorder the terms: 0 = (7 + 9x)(6x + 4) Reorder the terms: 0 = (7 + 9x)(4 + 6x) Multiply (7 + 9x) * (4 + 6x) 0 = (7(4 + 6x) + 9x * (4 + 6x)) 0 = ((4 * 7 + 6x * 7) + 9x * (4 + 6x)) 0 = ((28 + 42x) + 9x * (4 + 6x)) 0 = (28 + 42x + (4 * 9x + 6x * 9x)) 0 = (28 + 42x + (36x + 54x2)) Combine like terms: 42x + 36x = 78x 0 = (28 + 78x + 54x2) Solving 0 = 28 + 78x + 54x2 Solving for variable 'x'. Combine like terms: 0 + -28 = -28 -28 + -78x + -54x2 = 28 + 78x + 54x2 + -28 + -78x + -54x2 Reorder the terms: -28 + -78x + -54x2 = 28 + -28 + 78x + -78x + 54x2 + -54x2 Combine like terms: 28 + -28 = 0 -28 + -78x + -54x2 = 0 + 78x + -78x + 54x2 + -54x2 -28 + -78x + -54x2 = 78x + -78x + 54x2 + -54x2 Combine like terms: 78x + -78x = 0 -28 + -78x + -54x2 = 0 + 54x2 + -54x2 -28 + -78x + -54x2 = 54x2 + -54x2 Combine like terms: 54x2 + -54x2 = 0 -28 + -78x + -54x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(14 + 39x + 27x2) = 0 Factor a trinomial. -2((7 + 9x)(2 + 3x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(7 + 9x)' equal to zero and attempt to solve: Simplifying 7 + 9x = 0 Solving 7 + 9x = 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 + 9x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9x = 0 + -7 9x = 0 + -7 Combine like terms: 0 + -7 = -7 9x = -7 Divide each side by '9'. x = -0.7777777778 Simplifying x = -0.7777777778Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-0.7777777778, -0.6666666667}
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