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Simplifying 7x(x + 6) = 9x + 54 Reorder the terms: 7x(6 + x) = 9x + 54 (6 * 7x + x * 7x) = 9x + 54 (42x + 7x2) = 9x + 54 Reorder the terms: 42x + 7x2 = 54 + 9x Solving 42x + 7x2 = 54 + 9x Solving for variable 'x'. Reorder the terms: -54 + 42x + -9x + 7x2 = 54 + 9x + -54 + -9x Combine like terms: 42x + -9x = 33x -54 + 33x + 7x2 = 54 + 9x + -54 + -9x Reorder the terms: -54 + 33x + 7x2 = 54 + -54 + 9x + -9x Combine like terms: 54 + -54 = 0 -54 + 33x + 7x2 = 0 + 9x + -9x -54 + 33x + 7x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -54 + 33x + 7x2 = 0 Factor a trinomial. (-6 + -1x)(9 + -7x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(9 + -7x)' equal to zero and attempt to solve: Simplifying 9 + -7x = 0 Solving 9 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7x = 0 + -9 -7x = 0 + -9 Combine like terms: 0 + -9 = -9 -7x = -9 Divide each side by '-7'. x = 1.285714286 Simplifying x = 1.285714286Solution
x = {-6, 1.285714286}
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