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Simplifying (4x + -3)(6x + -3) = 0 Reorder the terms: (-3 + 4x)(6x + -3) = 0 Reorder the terms: (-3 + 4x)(-3 + 6x) = 0 Multiply (-3 + 4x) * (-3 + 6x) (-3(-3 + 6x) + 4x * (-3 + 6x)) = 0 ((-3 * -3 + 6x * -3) + 4x * (-3 + 6x)) = 0 ((9 + -18x) + 4x * (-3 + 6x)) = 0 (9 + -18x + (-3 * 4x + 6x * 4x)) = 0 (9 + -18x + (-12x + 24x2)) = 0 Combine like terms: -18x + -12x = -30x (9 + -30x + 24x2) = 0 Solving 9 + -30x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -10x + 8x2) = 0 Factor a trinomial. 3((1 + -2x)(3 + -4x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {0.5, 0.75}
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