=(5x+2)(7x+6)

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Solution for =(5x+2)(7x+6) equation:


Simplifying
0 = (5x + 2)(7x + 6)

Reorder the terms:
0 = (2 + 5x)(7x + 6)

Reorder the terms:
0 = (2 + 5x)(6 + 7x)

Multiply (2 + 5x) * (6 + 7x)
0 = (2(6 + 7x) + 5x * (6 + 7x))
0 = ((6 * 2 + 7x * 2) + 5x * (6 + 7x))
0 = ((12 + 14x) + 5x * (6 + 7x))
0 = (12 + 14x + (6 * 5x + 7x * 5x))
0 = (12 + 14x + (30x + 35x2))

Combine like terms: 14x + 30x = 44x
0 = (12 + 44x + 35x2)

Solving
0 = 12 + 44x + 35x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + -44x + -35x2 = 12 + 44x + 35x2 + -12 + -44x + -35x2

Reorder the terms:
-12 + -44x + -35x2 = 12 + -12 + 44x + -44x + 35x2 + -35x2

Combine like terms: 12 + -12 = 0
-12 + -44x + -35x2 = 0 + 44x + -44x + 35x2 + -35x2
-12 + -44x + -35x2 = 44x + -44x + 35x2 + -35x2

Combine like terms: 44x + -44x = 0
-12 + -44x + -35x2 = 0 + 35x2 + -35x2
-12 + -44x + -35x2 = 35x2 + -35x2

Combine like terms: 35x2 + -35x2 = 0
-12 + -44x + -35x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 44x + 35x2) = 0

Factor a trinomial.
-1((6 + 7x)(2 + 5x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(6 + 7x)' equal to zero and attempt to solve: Simplifying 6 + 7x = 0 Solving 6 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7x = 0 + -6 7x = 0 + -6 Combine like terms: 0 + -6 = -6 7x = -6 Divide each side by '7'. x = -0.8571428571 Simplifying x = -0.8571428571

Subproblem 2

Set the factor '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 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 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Divide each side by '5'. x = -0.4 Simplifying x = -0.4

Solution

x = {-0.8571428571, -0.4}

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