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Simplifying 4(2x + -3)(3x + 7) = 0 Reorder the terms: 4(-3 + 2x)(3x + 7) = 0 Reorder the terms: 4(-3 + 2x)(7 + 3x) = 0 Multiply (-3 + 2x) * (7 + 3x) 4(-3(7 + 3x) + 2x * (7 + 3x)) = 0 4((7 * -3 + 3x * -3) + 2x * (7 + 3x)) = 0 4((-21 + -9x) + 2x * (7 + 3x)) = 0 4(-21 + -9x + (7 * 2x + 3x * 2x)) = 0 4(-21 + -9x + (14x + 6x2)) = 0 Combine like terms: -9x + 14x = 5x 4(-21 + 5x + 6x2) = 0 (-21 * 4 + 5x * 4 + 6x2 * 4) = 0 (-84 + 20x + 24x2) = 0 Solving -84 + 20x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + 5x + 6x2) = 0 Factor a trinomial. 4((-7 + -3x)(3 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve: Simplifying -7 + -3x = 0 Solving -7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3x = 0 + 7 -3x = 0 + 7 Combine like terms: 0 + 7 = 7 -3x = 7 Divide each side by '-3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-2.333333333, 1.5}
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