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Simplifying 6[(4z + -3)(4z + -3)] + 7(4z + -3) + -3 = 0 Reorder the terms: 6[(-3 + 4z)(4z + -3)] + 7(4z + -3) + -3 = 0 Reorder the terms: 6[(-3 + 4z)(-3 + 4z)] + 7(4z + -3) + -3 = 0 Multiply (-3 + 4z) * (-3 + 4z) 6[(-3(-3 + 4z) + 4z * (-3 + 4z))] + 7(4z + -3) + -3 = 0 6[((-3 * -3 + 4z * -3) + 4z * (-3 + 4z))] + 7(4z + -3) + -3 = 0 6[((9 + -12z) + 4z * (-3 + 4z))] + 7(4z + -3) + -3 = 0 6[(9 + -12z + (-3 * 4z + 4z * 4z))] + 7(4z + -3) + -3 = 0 6[(9 + -12z + (-12z + 16z2))] + 7(4z + -3) + -3 = 0 Combine like terms: -12z + -12z = -24z 6[(9 + -24z + 16z2)] + 7(4z + -3) + -3 = 0 [9 * 6 + -24z * 6 + 16z2 * 6] + 7(4z + -3) + -3 = 0 [54 + -144z + 96z2] + 7(4z + -3) + -3 = 0 Reorder the terms: 54 + -144z + 96z2 + 7(-3 + 4z) + -3 = 0 54 + -144z + 96z2 + (-3 * 7 + 4z * 7) + -3 = 0 54 + -144z + 96z2 + (-21 + 28z) + -3 = 0 Reorder the terms: 54 + -21 + -3 + -144z + 28z + 96z2 = 0 Combine like terms: 54 + -21 = 33 33 + -3 + -144z + 28z + 96z2 = 0 Combine like terms: 33 + -3 = 30 30 + -144z + 28z + 96z2 = 0 Combine like terms: -144z + 28z = -116z 30 + -116z + 96z2 = 0 Solving 30 + -116z + 96z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -58z + 48z2) = 0 Factor a trinomial. 2((3 + -8z)(5 + -6z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -8z)' equal to zero and attempt to solve: Simplifying 3 + -8z = 0 Solving 3 + -8z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8z = 0 + -3 -8z = 0 + -3 Combine like terms: 0 + -3 = -3 -8z = -3 Divide each side by '-8'. z = 0.375 Simplifying z = 0.375Subproblem 2
Set the factor '(5 + -6z)' equal to zero and attempt to solve: Simplifying 5 + -6z = 0 Solving 5 + -6z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6z = 0 + -5 -6z = 0 + -5 Combine like terms: 0 + -5 = -5 -6z = -5 Divide each side by '-6'. z = 0.8333333333 Simplifying z = 0.8333333333Solution
z = {0.375, 0.8333333333}
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