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Simplifying 4x(x + -6) = 9(x + -6) Reorder the terms: 4x(-6 + x) = 9(x + -6) (-6 * 4x + x * 4x) = 9(x + -6) (-24x + 4x2) = 9(x + -6) Reorder the terms: -24x + 4x2 = 9(-6 + x) -24x + 4x2 = (-6 * 9 + x * 9) -24x + 4x2 = (-54 + 9x) Solving -24x + 4x2 = -54 + 9x Solving for variable 'x'. Reorder the terms: 54 + -24x + -9x + 4x2 = -54 + 9x + 54 + -9x Combine like terms: -24x + -9x = -33x 54 + -33x + 4x2 = -54 + 9x + 54 + -9x Reorder the terms: 54 + -33x + 4x2 = -54 + 54 + 9x + -9x Combine like terms: -54 + 54 = 0 54 + -33x + 4x2 = 0 + 9x + -9x 54 + -33x + 4x2 = 9x + -9x Combine like terms: 9x + -9x = 0 54 + -33x + 4x2 = 0 Factor a trinomial. (9 + -4x)(6 + -1x) = 0Subproblem 1
Set the factor '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 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 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25Subproblem 2
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 = 6Solution
x = {2.25, 6}
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