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Simplifying 4x(3 + a) + 20(a + 10) = 212a (3 * 4x + a * 4x) + 20(a + 10) = 212a Reorder the terms: (4ax + 12x) + 20(a + 10) = 212a (4ax + 12x) + 20(a + 10) = 212a Reorder the terms: 4ax + 12x + 20(10 + a) = 212a 4ax + 12x + (10 * 20 + a * 20) = 212a 4ax + 12x + (200 + 20a) = 212a Reorder the terms: 200 + 20a + 4ax + 12x = 212a Solving 200 + 20a + 4ax + 12x = 212a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-212a' to each side of the equation. 200 + 20a + 4ax + -212a + 12x = 212a + -212a Reorder the terms: 200 + 20a + -212a + 4ax + 12x = 212a + -212a Combine like terms: 20a + -212a = -192a 200 + -192a + 4ax + 12x = 212a + -212a Combine like terms: 212a + -212a = 0 200 + -192a + 4ax + 12x = 0 Add '-200' to each side of the equation. 200 + -192a + 4ax + -200 + 12x = 0 + -200 Reorder the terms: 200 + -200 + -192a + 4ax + 12x = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -192a + 4ax + 12x = 0 + -200 -192a + 4ax + 12x = 0 + -200 Combine like terms: 0 + -200 = -200 -192a + 4ax + 12x = -200 Add '-12x' to each side of the equation. -192a + 4ax + 12x + -12x = -200 + -12x Combine like terms: 12x + -12x = 0 -192a + 4ax + 0 = -200 + -12x -192a + 4ax = -200 + -12x Reorder the terms: 200 + -192a + 4ax + 12x = -200 + -12x + 200 + 12x Reorder the terms: 200 + -192a + 4ax + 12x = -200 + 200 + -12x + 12x Combine like terms: -200 + 200 = 0 200 + -192a + 4ax + 12x = 0 + -12x + 12x 200 + -192a + 4ax + 12x = -12x + 12x Combine like terms: -12x + 12x = 0 200 + -192a + 4ax + 12x = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(50 + -48a + ax + 3x) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(50 + -48a + ax + 3x)' equal to zero and attempt to solve: Simplifying 50 + -48a + ax + 3x = 0 Solving 50 + -48a + ax + 3x = 0 Move all terms containing a to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -48a + ax + -50 + 3x = 0 + -50 Reorder the terms: 50 + -50 + -48a + ax + 3x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -48a + ax + 3x = 0 + -50 -48a + ax + 3x = 0 + -50 Combine like terms: 0 + -50 = -50 -48a + ax + 3x = -50 Add '-3x' to each side of the equation. -48a + ax + 3x + -3x = -50 + -3x Combine like terms: 3x + -3x = 0 -48a + ax + 0 = -50 + -3x -48a + ax = -50 + -3x 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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