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Simplifying 4(2a + -3)(2a + -3) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 Reorder the terms: 4(-3 + 2a)(2a + -3) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 Reorder the terms: 4(-3 + 2a)(-3 + 2a) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 Multiply (-3 + 2a) * (-3 + 2a) 4(-3(-3 + 2a) + 2a * (-3 + 2a)) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 4((-3 * -3 + 2a * -3) + 2a * (-3 + 2a)) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 4((9 + -6a) + 2a * (-3 + 2a)) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 4(9 + -6a + (-3 * 2a + 2a * 2a)) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 4(9 + -6a + (-6a + 4a2)) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 Combine like terms: -6a + -6a = -12a 4(9 + -12a + 4a2) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 (9 * 4 + -12a * 4 + 4a2 * 4) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 (36 + -48a + 16a2) + -3(2a + -3)(a + -1) + -7(a + -1)(a + -1) = 0 Reorder the terms: 36 + -48a + 16a2 + -3(-3 + 2a)(a + -1) + -7(a + -1)(a + -1) = 0 Reorder the terms: 36 + -48a + 16a2 + -3(-3 + 2a)(-1 + a) + -7(a + -1)(a + -1) = 0 Multiply (-3 + 2a) * (-1 + a) 36 + -48a + 16a2 + -3(-3(-1 + a) + 2a * (-1 + a)) + -7(a + -1)(a + -1) = 0 36 + -48a + 16a2 + -3((-1 * -3 + a * -3) + 2a * (-1 + a)) + -7(a + -1)(a + -1) = 0 36 + -48a + 16a2 + -3((3 + -3a) + 2a * (-1 + a)) + -7(a + -1)(a + -1) = 0 36 + -48a + 16a2 + -3(3 + -3a + (-1 * 2a + a * 2a)) + -7(a + -1)(a + -1) = 0 36 + -48a + 16a2 + -3(3 + -3a + (-2a + 2a2)) + -7(a + -1)(a + -1) = 0 Combine like terms: -3a + -2a = -5a 36 + -48a + 16a2 + -3(3 + -5a + 2a2) + -7(a + -1)(a + -1) = 0 36 + -48a + 16a2 + (3 * -3 + -5a * -3 + 2a2 * -3) + -7(a + -1)(a + -1) = 0 36 + -48a + 16a2 + (-9 + 15a + -6a2) + -7(a + -1)(a + -1) = 0 Reorder the terms: 36 + -48a + 16a2 + -9 + 15a + -6a2 + -7(-1 + a)(a + -1) = 0 Reorder the terms: 36 + -48a + 16a2 + -9 + 15a + -6a2 + -7(-1 + a)(-1 + a) = 0 Multiply (-1 + a) * (-1 + a) 36 + -48a + 16a2 + -9 + 15a + -6a2 + -7(-1(-1 + a) + a(-1 + a)) = 0 36 + -48a + 16a2 + -9 + 15a + -6a2 + -7((-1 * -1 + a * -1) + a(-1 + a)) = 0 36 + -48a + 16a2 + -9 + 15a + -6a2 + -7((1 + -1a) + a(-1 + a)) = 0 36 + -48a + 16a2 + -9 + 15a + -6a2 + -7(1 + -1a + (-1 * a + a * a)) = 0 36 + -48a + 16a2 + -9 + 15a + -6a2 + -7(1 + -1a + (-1a + a2)) = 0 Combine like terms: -1a + -1a = -2a 36 + -48a + 16a2 + -9 + 15a + -6a2 + -7(1 + -2a + a2) = 0 36 + -48a + 16a2 + -9 + 15a + -6a2 + (1 * -7 + -2a * -7 + a2 * -7) = 0 36 + -48a + 16a2 + -9 + 15a + -6a2 + (-7 + 14a + -7a2) = 0 Reorder the terms: 36 + -9 + -7 + -48a + 15a + 14a + 16a2 + -6a2 + -7a2 = 0 Combine like terms: 36 + -9 = 27 27 + -7 + -48a + 15a + 14a + 16a2 + -6a2 + -7a2 = 0 Combine like terms: 27 + -7 = 20 20 + -48a + 15a + 14a + 16a2 + -6a2 + -7a2 = 0 Combine like terms: -48a + 15a = -33a 20 + -33a + 14a + 16a2 + -6a2 + -7a2 = 0 Combine like terms: -33a + 14a = -19a 20 + -19a + 16a2 + -6a2 + -7a2 = 0 Combine like terms: 16a2 + -6a2 = 10a2 20 + -19a + 10a2 + -7a2 = 0 Combine like terms: 10a2 + -7a2 = 3a2 20 + -19a + 3a2 = 0 Solving 20 + -19a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + -3a)(5 + -1a) = 0Subproblem 1
Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5Solution
a = {1.333333333, 5}
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