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Simplifying (7x + 4)(8x + 6) = 0 Reorder the terms: (4 + 7x)(8x + 6) = 0 Reorder the terms: (4 + 7x)(6 + 8x) = 0 Multiply (4 + 7x) * (6 + 8x) (4(6 + 8x) + 7x * (6 + 8x)) = 0 ((6 * 4 + 8x * 4) + 7x * (6 + 8x)) = 0 ((24 + 32x) + 7x * (6 + 8x)) = 0 (24 + 32x + (6 * 7x + 8x * 7x)) = 0 (24 + 32x + (42x + 56x2)) = 0 Combine like terms: 32x + 42x = 74x (24 + 74x + 56x2) = 0 Solving 24 + 74x + 56x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 37x + 28x2) = 0 Factor a trinomial. 2((3 + 4x)(4 + 7x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Subproblem 2
Set the factor '(4 + 7x)' equal to zero and attempt to solve: Simplifying 4 + 7x = 0 Solving 4 + 7x = 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 + 7x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7x = 0 + -4 7x = 0 + -4 Combine like terms: 0 + -4 = -4 7x = -4 Divide each side by '7'. x = -0.5714285714 Simplifying x = -0.5714285714Solution
x = {-0.75, -0.5714285714}
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