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Simplifying 6x(x + 5x) + -2 * 3 * 3 = 25x(7 + -13) + 6 * 6 Combine like terms: x + 5x = 6x 6x(6x) + -2 * 3 * 3 = 25x(7 + -13) + 6 * 6 Remove parenthesis around (6x) 6x * 6x + -2 * 3 * 3 = 25x(7 + -13) + 6 * 6 Reorder the terms for easier multiplication: 6 * 6x * x + -2 * 3 * 3 = 25x(7 + -13) + 6 * 6 Multiply 6 * 6 36x * x + -2 * 3 * 3 = 25x(7 + -13) + 6 * 6 Multiply x * x 36x2 + -2 * 3 * 3 = 25x(7 + -13) + 6 * 6 Multiply -2 * 3 36x2 + -6 * 3 = 25x(7 + -13) + 6 * 6 Multiply -6 * 3 36x2 + -18 = 25x(7 + -13) + 6 * 6 Reorder the terms: -18 + 36x2 = 25x(7 + -13) + 6 * 6 Combine like terms: 7 + -13 = -6 -18 + 36x2 = 25x(-6) + 6 * 6 Reorder the terms for easier multiplication: -18 + 36x2 = 25 * -6x + 6 * 6 Multiply 25 * -6 -18 + 36x2 = -150x + 6 * 6 Multiply 6 * 6 -18 + 36x2 = -150x + 36 Reorder the terms: -18 + 36x2 = 36 + -150x Solving -18 + 36x2 = 36 + -150x Solving for variable 'x'. Reorder the terms: -18 + -36 + 150x + 36x2 = 36 + -150x + -36 + 150x Combine like terms: -18 + -36 = -54 -54 + 150x + 36x2 = 36 + -150x + -36 + 150x Reorder the terms: -54 + 150x + 36x2 = 36 + -36 + -150x + 150x Combine like terms: 36 + -36 = 0 -54 + 150x + 36x2 = 0 + -150x + 150x -54 + 150x + 36x2 = -150x + 150x Combine like terms: -150x + 150x = 0 -54 + 150x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-9 + 25x + 6x2) = 0 Factor a trinomial. 6((-9 + -2x)(1 + -3x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 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 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-4.5, 0.3333333333}
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