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Simplifying (7x + -2)(x + 6) = 41x + -12 Reorder the terms: (-2 + 7x)(x + 6) = 41x + -12 Reorder the terms: (-2 + 7x)(6 + x) = 41x + -12 Multiply (-2 + 7x) * (6 + x) (-2(6 + x) + 7x * (6 + x)) = 41x + -12 ((6 * -2 + x * -2) + 7x * (6 + x)) = 41x + -12 ((-12 + -2x) + 7x * (6 + x)) = 41x + -12 (-12 + -2x + (6 * 7x + x * 7x)) = 41x + -12 (-12 + -2x + (42x + 7x2)) = 41x + -12 Combine like terms: -2x + 42x = 40x (-12 + 40x + 7x2) = 41x + -12 Reorder the terms: -12 + 40x + 7x2 = -12 + 41x Add '12' to each side of the equation. -12 + 40x + 12 + 7x2 = -12 + 12 + 41x Reorder the terms: -12 + 12 + 40x + 7x2 = -12 + 12 + 41x Combine like terms: -12 + 12 = 0 0 + 40x + 7x2 = -12 + 12 + 41x 40x + 7x2 = -12 + 12 + 41x Combine like terms: -12 + 12 = 0 40x + 7x2 = 0 + 41x 40x + 7x2 = 41x Solving 40x + 7x2 = 41x Solving for variable 'x'. Reorder the terms: 40x + -41x + 7x2 = 41x + -41x Combine like terms: 40x + -41x = -1x -1x + 7x2 = 41x + -41x Combine like terms: 41x + -41x = 0 -1x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 7x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1 + 7x)' equal to zero and attempt to solve: Simplifying -1 + 7x = 0 Solving -1 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 7x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 7x = 0 + 1 7x = 0 + 1 Combine like terms: 0 + 1 = 1 7x = 1 Divide each side by '7'. x = 0.1428571429 Simplifying x = 0.1428571429Solution
x = {0, 0.1428571429}
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