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Simplifying (4b + -7) * 6(8a + -7) * 8 = 40 Reorder the terms: (-7 + 4b) * 6(8a + -7) * 8 = 40 Reorder the terms: (-7 + 4b) * 6(-7 + 8a) * 8 = 40 Reorder the terms for easier multiplication: 6 * 8(-7 + 4b)(-7 + 8a) = 40 Multiply 6 * 8 48(-7 + 4b)(-7 + 8a) = 40 Multiply (-7 + 4b) * (-7 + 8a) 48(-7(-7 + 8a) + 4b * (-7 + 8a)) = 40 48((-7 * -7 + 8a * -7) + 4b * (-7 + 8a)) = 40 48((49 + -56a) + 4b * (-7 + 8a)) = 40 48(49 + -56a + (-7 * 4b + 8a * 4b)) = 40 Reorder the terms: 48(49 + -56a + (32ab + -28b)) = 40 48(49 + -56a + (32ab + -28b)) = 40 48(49 + -56a + 32ab + -28b) = 40 (49 * 48 + -56a * 48 + 32ab * 48 + -28b * 48) = 40 (2352 + -2688a + 1536ab + -1344b) = 40 Solving 2352 + -2688a + 1536ab + -1344b = 40 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2352' to each side of the equation. 2352 + -2688a + 1536ab + -2352 + -1344b = 40 + -2352 Reorder the terms: 2352 + -2352 + -2688a + 1536ab + -1344b = 40 + -2352 Combine like terms: 2352 + -2352 = 0 0 + -2688a + 1536ab + -1344b = 40 + -2352 -2688a + 1536ab + -1344b = 40 + -2352 Combine like terms: 40 + -2352 = -2312 -2688a + 1536ab + -1344b = -2312 Add '1344b' to each side of the equation. -2688a + 1536ab + -1344b + 1344b = -2312 + 1344b Combine like terms: -1344b + 1344b = 0 -2688a + 1536ab + 0 = -2312 + 1344b -2688a + 1536ab = -2312 + 1344b Reorder the terms: 2312 + -2688a + 1536ab + -1344b = -2312 + 1344b + 2312 + -1344b Reorder the terms: 2312 + -2688a + 1536ab + -1344b = -2312 + 2312 + 1344b + -1344b Combine like terms: -2312 + 2312 = 0 2312 + -2688a + 1536ab + -1344b = 0 + 1344b + -1344b 2312 + -2688a + 1536ab + -1344b = 1344b + -1344b Combine like terms: 1344b + -1344b = 0 2312 + -2688a + 1536ab + -1344b = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(289 + -336a + 192ab + -168b) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(289 + -336a + 192ab + -168b)' equal to zero and attempt to solve: Simplifying 289 + -336a + 192ab + -168b = 0 Solving 289 + -336a + 192ab + -168b = 0 Move all terms containing a to the left, all other terms to the right. Add '-289' to each side of the equation. 289 + -336a + 192ab + -289 + -168b = 0 + -289 Reorder the terms: 289 + -289 + -336a + 192ab + -168b = 0 + -289 Combine like terms: 289 + -289 = 0 0 + -336a + 192ab + -168b = 0 + -289 -336a + 192ab + -168b = 0 + -289 Combine like terms: 0 + -289 = -289 -336a + 192ab + -168b = -289 Add '168b' to each side of the equation. -336a + 192ab + -168b + 168b = -289 + 168b Combine like terms: -168b + 168b = 0 -336a + 192ab + 0 = -289 + 168b -336a + 192ab = -289 + 168b The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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