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Simplifying 2x2(5 + -1x)(7x + 3) = 0 Reorder the terms: 2x2(5 + -1x)(3 + 7x) = 0 Multiply (5 + -1x) * (3 + 7x) 2x2(5(3 + 7x) + -1x * (3 + 7x)) = 0 2x2((3 * 5 + 7x * 5) + -1x * (3 + 7x)) = 0 2x2((15 + 35x) + -1x * (3 + 7x)) = 0 2x2(15 + 35x + (3 * -1x + 7x * -1x)) = 0 2x2(15 + 35x + (-3x + -7x2)) = 0 Combine like terms: 35x + -3x = 32x 2x2(15 + 32x + -7x2) = 0 (15 * 2x2 + 32x * 2x2 + -7x2 * 2x2) = 0 (30x2 + 64x3 + -14x4) = 0 Solving 30x2 + 64x3 + -14x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(15 + 32x + -7x2) = 0 Factor a trinomial. 2x2((5 + -1x)(3 + 7x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 3
Set the factor '(3 + 7x)' equal to zero and attempt to solve: Simplifying 3 + 7x = 0 Solving 3 + 7x = 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 + 7x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7x = 0 + -3 7x = 0 + -3 Combine like terms: 0 + -3 = -3 7x = -3 Divide each side by '7'. x = -0.4285714286 Simplifying x = -0.4285714286Solution
x = {0, 5, -0.4285714286}
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