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Simplifying (2x + 1)(7x + -42) = 15x + -120 Reorder the terms: (1 + 2x)(7x + -42) = 15x + -120 Reorder the terms: (1 + 2x)(-42 + 7x) = 15x + -120 Multiply (1 + 2x) * (-42 + 7x) (1(-42 + 7x) + 2x * (-42 + 7x)) = 15x + -120 ((-42 * 1 + 7x * 1) + 2x * (-42 + 7x)) = 15x + -120 ((-42 + 7x) + 2x * (-42 + 7x)) = 15x + -120 (-42 + 7x + (-42 * 2x + 7x * 2x)) = 15x + -120 (-42 + 7x + (-84x + 14x2)) = 15x + -120 Combine like terms: 7x + -84x = -77x (-42 + -77x + 14x2) = 15x + -120 Reorder the terms: -42 + -77x + 14x2 = -120 + 15x Solving -42 + -77x + 14x2 = -120 + 15x Solving for variable 'x'. Reorder the terms: -42 + 120 + -77x + -15x + 14x2 = -120 + 15x + 120 + -15x Combine like terms: -42 + 120 = 78 78 + -77x + -15x + 14x2 = -120 + 15x + 120 + -15x Combine like terms: -77x + -15x = -92x 78 + -92x + 14x2 = -120 + 15x + 120 + -15x Reorder the terms: 78 + -92x + 14x2 = -120 + 120 + 15x + -15x Combine like terms: -120 + 120 = 0 78 + -92x + 14x2 = 0 + 15x + -15x 78 + -92x + 14x2 = 15x + -15x Combine like terms: 15x + -15x = 0 78 + -92x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(39 + -46x + 7x2) = 0 Factor a trinomial. 2((1 + -1x)(39 + -7x)) = 0 Ignore the factor 2.Subproblem 1
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 = 1Subproblem 2
Set the factor '(39 + -7x)' equal to zero and attempt to solve: Simplifying 39 + -7x = 0 Solving 39 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + -7x = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -7x = 0 + -39 -7x = 0 + -39 Combine like terms: 0 + -39 = -39 -7x = -39 Divide each side by '-7'. x = 5.571428571 Simplifying x = 5.571428571Solution
x = {1, 5.571428571}
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