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Simplifying (6x + -3)(5x + 4) = 0 Reorder the terms: (-3 + 6x)(5x + 4) = 0 Reorder the terms: (-3 + 6x)(4 + 5x) = 0 Multiply (-3 + 6x) * (4 + 5x) (-3(4 + 5x) + 6x * (4 + 5x)) = 0 ((4 * -3 + 5x * -3) + 6x * (4 + 5x)) = 0 ((-12 + -15x) + 6x * (4 + 5x)) = 0 (-12 + -15x + (4 * 6x + 5x * 6x)) = 0 (-12 + -15x + (24x + 30x2)) = 0 Combine like terms: -15x + 24x = 9x (-12 + 9x + 30x2) = 0 Solving -12 + 9x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 3x + 10x2) = 0 Factor a trinomial. 3((-4 + -5x)(1 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -5x)' equal to zero and attempt to solve: Simplifying -4 + -5x = 0 Solving -4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5x = 0 + 4 -5x = 0 + 4 Combine like terms: 0 + 4 = 4 -5x = 4 Divide each side by '-5'. x = -0.8 Simplifying x = -0.8Subproblem 2
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 = 0.5Solution
x = {-0.8, 0.5}
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