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Simplifying 0 = (5x + -7)(3x + -2) Reorder the terms: 0 = (-7 + 5x)(3x + -2) Reorder the terms: 0 = (-7 + 5x)(-2 + 3x) Multiply (-7 + 5x) * (-2 + 3x) 0 = (-7(-2 + 3x) + 5x * (-2 + 3x)) 0 = ((-2 * -7 + 3x * -7) + 5x * (-2 + 3x)) 0 = ((14 + -21x) + 5x * (-2 + 3x)) 0 = (14 + -21x + (-2 * 5x + 3x * 5x)) 0 = (14 + -21x + (-10x + 15x2)) Combine like terms: -21x + -10x = -31x 0 = (14 + -31x + 15x2) Solving 0 = 14 + -31x + 15x2 Solving for variable 'x'. Combine like terms: 0 + -14 = -14 -14 + 31x + -15x2 = 14 + -31x + 15x2 + -14 + 31x + -15x2 Reorder the terms: -14 + 31x + -15x2 = 14 + -14 + -31x + 31x + 15x2 + -15x2 Combine like terms: 14 + -14 = 0 -14 + 31x + -15x2 = 0 + -31x + 31x + 15x2 + -15x2 -14 + 31x + -15x2 = -31x + 31x + 15x2 + -15x2 Combine like terms: -31x + 31x = 0 -14 + 31x + -15x2 = 0 + 15x2 + -15x2 -14 + 31x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -14 + 31x + -15x2 = 0 Factor a trinomial. (-7 + 5x)(2 + -3x) = 0Subproblem 1
Set the factor '(-7 + 5x)' equal to zero and attempt to solve: Simplifying -7 + 5x = 0 Solving -7 + 5x = 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 + 5x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5x = 0 + 7 5x = 0 + 7 Combine like terms: 0 + 7 = 7 5x = 7 Divide each side by '5'. x = 1.4 Simplifying x = 1.4Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {1.4, 0.6666666667}
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