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Simplifying -4(5a + -6b) + 7(2ab + -4b2) = 0 (5a * -4 + -6b * -4) + 7(2ab + -4b2) = 0 (-20a + 24b) + 7(2ab + -4b2) = 0 -20a + 24b + (2ab * 7 + -4b2 * 7) = 0 -20a + 24b + (14ab + -28b2) = 0 Reorder the terms: -20a + 14ab + 24b + -28b2 = 0 Solving -20a + 14ab + 24b + -28b2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-24b' to each side of the equation. -20a + 14ab + 24b + -24b + -28b2 = 0 + -24b Combine like terms: 24b + -24b = 0 -20a + 14ab + 0 + -28b2 = 0 + -24b -20a + 14ab + -28b2 = 0 + -24b Remove the zero: -20a + 14ab + -28b2 = -24b Add '28b2' to each side of the equation. -20a + 14ab + -28b2 + 28b2 = -24b + 28b2 Combine like terms: -28b2 + 28b2 = 0 -20a + 14ab + 0 = -24b + 28b2 -20a + 14ab = -24b + 28b2 Reorder the terms: -20a + 14ab + 24b + -28b2 = -24b + 24b + 28b2 + -28b2 Combine like terms: -24b + 24b = 0 -20a + 14ab + 24b + -28b2 = 0 + 28b2 + -28b2 -20a + 14ab + 24b + -28b2 = 28b2 + -28b2 Combine like terms: 28b2 + -28b2 = 0 -20a + 14ab + 24b + -28b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10a + 7ab + 12b + -14b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10a + 7ab + 12b + -14b2)' equal to zero and attempt to solve: Simplifying -10a + 7ab + 12b + -14b2 = 0 Solving -10a + 7ab + 12b + -14b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-12b' to each side of the equation. -10a + 7ab + 12b + -12b + -14b2 = 0 + -12b Combine like terms: 12b + -12b = 0 -10a + 7ab + 0 + -14b2 = 0 + -12b -10a + 7ab + -14b2 = 0 + -12b Remove the zero: -10a + 7ab + -14b2 = -12b Add '14b2' to each side of the equation. -10a + 7ab + -14b2 + 14b2 = -12b + 14b2 Combine like terms: -14b2 + 14b2 = 0 -10a + 7ab + 0 = -12b + 14b2 -10a + 7ab = -12b + 14b2 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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