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Simplifying (5x + 3) * 6(30b + -15a) = 0 Reorder the terms: (3 + 5x) * 6(30b + -15a) = 0 Reorder the terms: (3 + 5x) * 6(-15a + 30b) = 0 Reorder the terms for easier multiplication: 6(3 + 5x)(-15a + 30b) = 0 Multiply (3 + 5x) * (-15a + 30b) 6(3(-15a + 30b) + 5x * (-15a + 30b)) = 0 6((-15a * 3 + 30b * 3) + 5x * (-15a + 30b)) = 0 6((-45a + 90b) + 5x * (-15a + 30b)) = 0 6(-45a + 90b + (-15a * 5x + 30b * 5x)) = 0 6(-45a + 90b + (-75ax + 150bx)) = 0 Reorder the terms: 6(-45a + -75ax + 90b + 150bx) = 0 6(-45a + -75ax + 90b + 150bx) = 0 (-45a * 6 + -75ax * 6 + 90b * 6 + 150bx * 6) = 0 (-270a + -450ax + 540b + 900bx) = 0 Solving -270a + -450ax + 540b + 900bx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-540b' to each side of the equation. -270a + -450ax + 540b + -540b + 900bx = 0 + -540b Combine like terms: 540b + -540b = 0 -270a + -450ax + 0 + 900bx = 0 + -540b -270a + -450ax + 900bx = 0 + -540b Remove the zero: -270a + -450ax + 900bx = -540b Add '-900bx' to each side of the equation. -270a + -450ax + 900bx + -900bx = -540b + -900bx Combine like terms: 900bx + -900bx = 0 -270a + -450ax + 0 = -540b + -900bx -270a + -450ax = -540b + -900bx Reorder the terms: -270a + -450ax + 540b + 900bx = -540b + 540b + -900bx + 900bx Combine like terms: -540b + 540b = 0 -270a + -450ax + 540b + 900bx = 0 + -900bx + 900bx -270a + -450ax + 540b + 900bx = -900bx + 900bx Combine like terms: -900bx + 900bx = 0 -270a + -450ax + 540b + 900bx = 0 Factor out the Greatest Common Factor (GCF), '90'. 90(-3a + -5ax + 6b + 10bx) = 0 Ignore the factor 90.Subproblem 1
Set the factor '(-3a + -5ax + 6b + 10bx)' equal to zero and attempt to solve: Simplifying -3a + -5ax + 6b + 10bx = 0 Solving -3a + -5ax + 6b + 10bx = 0 Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. -3a + -5ax + 6b + -6b + 10bx = 0 + -6b Combine like terms: 6b + -6b = 0 -3a + -5ax + 0 + 10bx = 0 + -6b -3a + -5ax + 10bx = 0 + -6b Remove the zero: -3a + -5ax + 10bx = -6b Add '-10bx' to each side of the equation. -3a + -5ax + 10bx + -10bx = -6b + -10bx Combine like terms: 10bx + -10bx = 0 -3a + -5ax + 0 = -6b + -10bx -3a + -5ax = -6b + -10bx 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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